THE  LIBRARY 

OF 

THE  UNIVERSITY 

OF  CALIFORNIA 

LOS  ANGELES 


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The 
Refractive  and  Motor  Mechanism 

of  the  Eye 


BY 


WILLIAM  NORWOOD  SOUTER,  M.D. 

ASSOCIATE  OPHTHALMOLOGIST,  EPISCOPAL  EYE,  EAR 
AND  THROAT  HOSPITAL,  WASHINGTON,  D.  C. 


WITH  148  ILLUSTRATIONS 


THE  KEYSTONE  PUBLISHING  CO. 

PHILADELPHIA,   U.  S.  A. 

1910 


COPYRIGHT,   1910,   BY 
THE  KEYSTONE  PUBLISHINGlCO 


fJL»V» 


CONTENTS  Iqr6 


CHAPTER  I 

Vision  and  Light 13-21 

Vision — Light — Theories  of  the  Transmission  of  Light — Color 
—Velocity  of  Light,  Wave  Length,  Vibratory  Period — Lu- 
minosity— Wave  Front — Pencils  and  Rays — Superposition  of 
Waves — Formation  of  Images. 


CHAPTER  II 

The    Laws    of    Refraction    and    Reflection;    Refraction    and 

Reflection  at  Plane  Surfaces 22-35 

The  Law  of  Refraction — Passage  of  Light  Through  a  Medium 
Bounded  by  Two  Parallel  Surfaces — Prisms — Refraction  of 
Parallel  Rays  by  a  Prism — Minimum  Deviation — Refraction 
of  a  Spherical  Wave  (Divergent  Rays)  by  a  Prism — Disper- 
sion of  Colors — Numeration  of  Prisms — Combination  of 
Prisms — Reflection — The  Law  of  Reflection — Reflection  at 
Plane  Surfaces — Total  Reflection. 


CHAPTER  III 

Refraction  and  Reflection  at  Spherical  Surfaces 36-53 

Summary  of  Collective  Refraction — Dispersive  Refraction — 
Aberration — Algebraic  Relation  Between  Conjugate  Foci — 
Formation  of  Images  by  Refraction — Relative  Size  of  Object 
and  Image — Cardinal  Points  and  Planes — Spherical  Lenses — 
Convex  Lenses — Concave  Lenses — Cardinal  Points  of  Lenses 
— Algebraic  Relation  Between  Conjugate  Foci  in  Lens  Re- 
fraction— Numeration  of  Lenses — Reflection  at  Spherical 
Surfaces — x\Igebraic  Relation  Between  Conjugate  Foci  in 
Reflection. 

CHAPTER  IV 

Compound  Optical  Systems 54-63 

Cardinal  Points  of  a  Compound  System — The  Eye — Formation 
of  Tmages  by  the  Eye — Relative   Size  of  Object  and  Image — 


Table  of  Contents 

The  Visual  Angle — The  Schematic  Eye — The  Reduced  Eye — 
The  Aphakic  Eye — Relative  Position  of  the  Retina  and  Pos- 
terior Principal  Focus  of  the  Eye — Accommodation. 


CHAPTER  V 

Refraction  at  Asymmetrical  Surfaces 64-72 

Principal  Meridians — The  Toric  Surface — Image  of  a  Point 
in  Asymmetrical  Refraction — Image  of  a  Line  in  Asymmetrical 
Refraction — The  Toric  Lens — The  Cylindrical  Lens — Notation 
of  Toric  and  Cylindrical  Lenses — Combination  of  Cylindrical 
Lenses — Asymmetry  of  Oblique  Refraction — Asymmetry  of 
Prismatic  Refraction. 

CHAPTER  VI 

Correction  of  Optical  Defects  of  the  Eye  by  Lenses 73-86 

Use  of  Spherical  Lenses — Far  Point  of  the  Eye — Effect  of 
Changing  the  Position  of  the  Correcting  Lens — Measurement 
of  Ametropia  by  the  Correcting  Lens — Effect  of  Lenses  Upon 
the  Size  of  Retinal  Images — Enlargement  of  Images  Effected 
by  Removal  of  the  Crystalline  Lens — Length  of  Axis  in  Ame- 
tropia— Axial  Length  of  the  Eye  in  Relation  to  the  Probable 
Refractive  Condition  After  Removal  of  the  Lens — Correction 
of  Astigmia — Distortion  of  Images  in  Astigmia — Determina- 
tion of  the  Axis  of  a  Cylindrical  Lens. 

CHAPTER  VII 

Optical   Principles   of   Ophthalmoscopy,   Skiascopy  and   Oph- 
thalmometry   87-1 10 

Indirect  Method  of  Ophthalmoscopy — Direct  Method  of  Oph- 
thalmoscopy— Skiascopy — Point  of  Reversal — Reversal  of 
Movement — Variation  of  Magnification— Movement  of  the 
Shadow  Line — Form  of  the  Shadow  Line — Illumination  of  the 
Retina — Two  Points  of  Reversal  in  Astigmia — Rectilinear 
Shadow  Lines  in  Astigmia — Summary  of  Underlying  Prin- 
ciples of  Skiascopy — Ophthalmometry — Keratometry  and 
Phakometry — Determination  of  Astigmia  by  Ophthalmometry. 


CHAPTER  VIII 

The  Refractive  Mechanism 111-142 

The  External  Coat — The  Uvea — The  Retina — Contents  of  the 
Eyeball — Surfaces  and  Media  of  the  Eye — Insensitiveness  of 


Table  of  Contents 

the  Periphery  of  the  Retina — Alpha  and  Gamma— The  Iris— 
Choroidal  and  Retinal  Pigment — Refraction  of  the  Eye — 
Emmetropia — Accommodation — The  Ciliary  Region — Helm- 
holtz's  Theory — Experimental  Observations — Tscherning's 
Theory — Length  of  Time  Required  for  Accommodation — 
Range  of  Accommodation — Reserve  Accommodation. 


CHAPTER  IX 

The  Motor  Mechanism 143-160. 

The  Extrinsic  Muscles  of  the  Eye — Nerve  Supply  of  the  Ex- 
trinsic Muscles — Ocular  Motions — Center  of  Rotation — Field 
of  Fixation — Binocular  Fixation — Conjugate  Movements — 
Listing's  Law — Convergence — Measurement  of  Convergence — 
Near  Point  of  Convergence — Relaxation  of  Convergence — 
Far  Point  of  Convergence — Association  of  Accommodation 
and  Convergence — Accommodation  and  Convergence  in  Side 
Vision — The  Horopter — Normal   Muscular  Equilibrium. 


CHAPTER  X 

Optometry  of  the  Refractive  Apparatus 161-195 

Subjective  Methods — Optometers  Based  Upon  the  Action  of  a 
Convex  Lens — Optometers  Based  Upon  the  Principle  of  the 
Opera  Glass  or  Galileo's  Telescope — Optometers  Based  Upon 
Scheiner's  Experiment — Optometers  Based  Upon  Chromatic 
Aberration — Optometers  Based  Upon  the  Measurement  of  the 
Retinal  Diffusion  Circles — Optometry  Based  Upon  Movement 
of  the  Diffusion  Image  on  the  Retina — Optometry  Based 
Upon  Visual  Acuteness — Objective  Methods — Indirect  Method 
of  Ophthalmoscopy — Skiascopy — Ophthalmometry. 


CHAPTER  XI 

Hyperopia 196-213; 

Curvature-Hyperopia — Index-Hyperopia — Axial  Hyperopia — 
Degree  of  Hyperopia — Low-grade  Hyperopia — Medium  Hyper- 
opia— High-grade  Hyperopia — Latent  and  Manifest  Hyperopia 
— Symptoms  of  Hyperopia — Objective  Symptoms — Diagnosis 
of  Hyperopia — Treatment  of  Hyperopia — Correction  of  Low- 
grade  Hyperopia  in  Childhood — Correction  of  Low-grade 
Hyperopia  in  Adult  Life — Correction  of  Medium  and  High- 
grade  Hyperopia — Treatment  of  Muscular  Disturbances — 
Secondary    Effects    of    Convex    Lenses — Enlargement    of    the- 


8  Table  of  Contents 

Retinal  Image — Apparent  Magnification  of  Objects — Altera- 
tion in  the  Relation  Between  Convergence  and  Accommodation 
— Prismatic  Action  of  Convex  Lenses — Prescription  of  Lenses 
— Verification  and  Adjustment  of  Lenses. 


CHAPTER  XII 

Myopia 214-236 

Curvature-Myopia — Index-Myopia — Axial  Myopia — The  Conus 
—Two  Theories  as  to  the  Origin  of  Posterior  Staphyloma— 
Anatomical  and  Ophthalmoscopic  Characteristics — Two  ..Types 
of  Axial  Myopia — Statistics  of  Myopia — Symptoms  of  Myopia 
— Divergent  Strabismus  in  Myopia — Symptoms  Arising  from 
Disturbed  Nutrition  in  Staphyloma — Diagnosis  of  Myopia — 
Differentiation  of  Mild  and  Malignant  Myopia — Diagnosis  of 
Curvature-Myopia  and  Index-Myopia — Treatment  of  Myopia — 
Prophylactic  Measures — Use  of  Lenses  in  Myopia- — Operative 
Treatment  of  Axial  Myopia — Operative  Treatment  of  Conical 
Cornea. 

CHAPTER  XIII 

ASTIGMIA 237-252 

Etiology  of  Corneal  Astigmia — Relation  of  Astigmia  to  Cranial 
Development — Change  in  the  Form  of  the  Cornea — Etiology 
of  Lenticular  Astigmia — Dynamic  Astigmia — Degree  of  As- 
tigmia— Classifications  of  Astigmia — Classification  with  Refer- 
ence to  the  Position  of  the  Principal  Meridians — Classification 
with  Reference  to  the  Relative  Directions  of  the  Principal 
Meridians  in  the  Two  Eyes — Classification  with  Reference  to 
the  Relation  Between  the  Position  of  the  Retina  and  that  of 
the  Focal  Lines — Symptoms  of  Astigmia — Vision  in  Astigmia 
— Asthenopia — Objective  Symptoms — Diagnosis  of  Astigmia — 
Treatment  of  Astigmia — Prescription  of  Compound  Lenses — 
Surgical  Treatment  of  Astigmia. 


CHAPTER  XIV 

Anisometropia    253-258 

Etiology — Vision  in  Anisometropia — Anisometropic  Asthenopia 
— Treatment. 

CHAPTER  XV 

Presbyopia  and  Anomalies  of  Accommodation 259-266 

Age    at     which     Presbyopia    Occurs — Symptoms — Diagnosis — 
Treatment — Spasm  of   Accommodation— Symptoms — Diagnosis 


Table  of  Contents 

— Treatment — Paresis  and  Paralysis  of  Accommodation — 
Diphtheritic  Paralysis — Syphilitic  Paralysis — Paralysis  Caused 
by  Non-Syphilitic  Brain  Lesion — Glaucomatous  Paralysis — Ac- 
ommodative  Paralysis  Arising  from  other  Diseases — Artificial 
Cycloplegia — Symptoms  and  Diagnosis  of  Accommodative 
Paralysis — Treatment  of  Accommodative  Paralysis — Loss  of 
Accommodation  from  Absence  or  Luxation  of  the  Lens. 


CHAPTER  XVI 

OMETRY    OF   THE    MOTOR    APPARATUS 267-29O 

Diplopia — Tests  Used  in  Motor  Optometry — Cover  Test — 
Duane's  Parallax  Test — Colored  Glass  Test — Graefe's  Test — 
Maddox  Rod  Test — Stenopeic  Lens  Test — Measurement  of 
Convergence  and  Divergence — Measurement  of  Prism  Con- 
vergence— Graefe's  Linear  Method — The  Perimeter  Method — 
Priestly  Smith's  Tape  Method — Maddox  Tangent  Scale — 
Measurement  of  the  Field  of  Fixation — Tests  of  Binocular 
Vision. 

CHAPTER  XVII 

Non-Paralytic  Disorders  of  Equilibrium 291-307 

Excess  of  Convergence — Etiology  of  Excessive  Convergence — 
Symptoms  of  Excessive  Convergence — Diagnosis  of  Excessive 
Convergence — Treatment  of  Excessive  Convergence — Defi- 
ciency of  Convergence — Etiology  of  Convergence  Deficiency — 
Symptoms  of  Convergence  Deficiency — Diagnosis  of  Converg- 
ence Deficiency— Treatment  of  Convergence  Deficiency — Ver- 
tical Imbalance — Etiology — Symptoms  and  Diagnosis — Treat- 
ment— Cyclophoria  and  Cyclotropia — Treatment — Anophoria, 
Anotropia;  Katophoria,  Katotropia — Spasmodic  Conjugate 
Deviation — Nystagmus — Etiology— Symptoms  and  Diagnosis — 
Treatment — Disorders  of  Motility  Caused  by  Mechanical  Im- 
pediment. 

CHAPTER  XVIII 
r  w.vtk   Disorders  of  Motility 308-325 

Paralyses  of  the  Ocular  Muscles — Etiology — General  Symp- 
toms— Paralysis  of  the  External  Rectus  (Sixth  Nerve)  — 
Paralysis  of  the  Internal  Rectus — Paralysis  of  the  Superior 
Rectus — Paralysis  of  the  Inferior  Rectus — Paralysis  of  the 
inferior  Oblique — Paralysis  of  the  Superior  Oblique — Paralysis 
of    the    Third     Nerve — Combined     Paralysis    of    the     Ocular 


io  Table  of  Contents 

Muscles — Diagnosis — Treatment — Paralyses  of  Associated 
Movements — Paralysis  of  Convergence — Paralysis  of  Diverg- 
ence— Treatment   of   Paralysis   of  Associated   Movements. 


APPENDIX 
Algebraic    Formulae 325-34" 

Deviation  Effected  by  a  Prism — Relation  Between  Conjugate 
Points  in  Refraction  at  a  Spherical  Surface — Principal  Foci 
and  Focal  Distances — Relation  Between  Conjugate  Points  in 
Refraction  by  Lenses— The  Cardinal  Points  of  the  Schematic 
Eye— Anterior  Principal  Focus— Posterior  Principal  Focus- 
First  Principal  Point— Second  Principal  Point— First  Nodal 
Point— Second  Nodal  Point— Principal  Focal  Distances— Car- 
dinal Points  of  a  Thick  Lens— Relation  Between  Variation 
of  Curvature  and  Astigmia — Ophthalmometric  Determination 
of  Astigmia  of  the  Crystalline  Lens — Relation  Between  As- 
tigmia Produced  at  the  Anterior  Surface  of  the  Crystalline 
Lens  and  the  Correcting  Lens  Placed  in  Front  of  the  Cornea 
— Relation  Between  Astigmia  Produced  at  the  Posterior  Sur- 
face of  the  Crystalline  Lens  and  the  Correcting  Lens  Placed 
in  Front  of  the  Cornea. 


The 

Refractive  and  Motor  Mechanism 

of  the  Eye 


PART  I 

PRINCIPLES    OF    OPTICS 

CHAPTER  I 
VISION   AND   LIGHT 

Vision  is  the  sense  which  reveals  to  us  the  form  and  color 
of  objects  by  the  action  of  light  on  the  retina;  in  other  words, 
vision  may  be  defined  as  the  consciousness  which  results  from 
the  stimulation  of  the  retina  by  light. 

The  visual  apparatus  consists  of  two  distinct  parts.  The  first 
of  these  is  the  eye,  which  is  analogous  to  a  photograph  camera. 
The  retina,  which  receives  and  transforms  the  light  energy 
into  a  nerve  impulse,  corresponds  to  the  sensitized  plate  of  the 
camera.  The  second  part  of  the  visual  apparatus  consists  of  the 
optic  nerve  and  its  brain  connections — the  conducting  and  inter- 
preting mechanism — by  means  of  which  the  nerve  impulse  is 
carried  to  the  visual  areas  of  the  brain  and  thence  to  the  centers 
of  consciousness,  where  the  impulse  is  manifested  as  vision. 

It  falls  within  our  province  in  this  work  io  deal  only  with 
the  former  part  of  this  apparatus — to  study  the  eye  as  an  optical 
contrivance  and  to  investigate  the  adaptability  and  the  imper- 
fections of  its  mechanism. 

Light,  the  physical  agency  by  which  we  see,  is  a  form  of 
energy.  The  science  of  physics  teaches  that  ultimately  all  energy 
is  one,  but  that  by  the  various  modifications  which  it  undergoes 
different  results  are  manifested  from  its  expenditure. 

Light  may  be  produced  in  various  ways,  as  by  mechanical  or 
chemical  action.  Although  light  artificially  produced  plays  an 
important  part  in  our  life,  our  chief  source  of  light  must  always 
be  the  sun. 

The  study  of  the  laws  of  light  constitutes  the  science  of 
optics.  In  its  various  branches  this  is  a  comprehensive  study, 
which  would  lead  us  far  beyond  the  province  of  ophthalmology. 

(13) 


14  Principles    of    Optics 

Only  a  small  part  of  the  science  of  optics  can,  therefore,  be  con- 
sidered in  this  work — that  part  which  pertains  to  the  reflection 
and,  more  especially,  to  the  refraction  of  light. 

A  substance  which  has  the  power  of  developing  light-energy, 
or  emitting  light,  is  said  to  be  luminous.  Thus  the  sun  is  a 
luminous  body.  On  the  other  hand,  the  moon,  which  does  not 
originate  light,  but  only  transmits  it  by  reflection  from  the  sun, 
is  a  non-luminous  body. 

Theories  of  the  Transmission  of  Light. — The  question 
as  to  the  manner  in  which  light  is  conveyed  from  a  luminous  body 
to  the  eye  has  given  rise  to  two  hypotheses,  which  are  known, 
respectively,  as  the  corpuscular  or  emission  theory  and  the  wave 
theory. 

The  corpuscular  theory  naturally  presented  itself  to  the 
ancients  and  was  universally  accepted  prior  to  the  development 
of  the  science  of  optics.  In  accordance  with  this  theory,  it  was 
believed  that  light  was  a  substance  given  off  from  a  luminous 
body  and  that  this  substance  was  propelled  in  all  directions  in 
straight  lines.  Sir  Isaac  Newton  was  an  advocate  of  this,  in 
opposition  to  the  second  hypothesis  (which  was  announced  by 
Huygens  in  1678),  because,  in  the  form  in  which  the  latter  was 
then  propounded,  it  failed  to  explain  certain  phenomena. 

The  second  hypothesis,  or  wave  theory,  as  enunciated  by 
Huygens  and  as  modified  by  subsequent  investigators,  satisfac- 
torily explains  all  the  observed  phenomena  of  light.  In  fact, 
certain  phenomena  which  follow  as  a  necessary  sequence  of  the 
wave  theory  were  discovered  through  study  of  this  theory,  the 
mathematical  demonstrations  which  led  to  such  discoveries  having 
afterward  been  corroborated  by  actual  experiment. 

Ether  is  the  extremely  tenuous  matter  which,  it  has  been 
assumed,  exists  throughout  the  universe.  It  is  only  by  the 
assumption  that  such  matter  exists  that  we  can  form  a  conception 
of  the  transmission  of  waves  through  space.  There  is  no  other 
evidence,  except  this  mental  requirement,  that  such  matter 
really  exists. 

A  familiar  example  of  a  wave  is  afforded  by  throwing  a 
stone  into  a  body  of  still  water.  In  this  case  and  in  sound-waves 
traveling  in  air  a  vibratory  motion  of  the  particles  of  the  con- 
ductor takes  place  in  the  direction  in  which  the  wave  is  moving. 
The   earlier   advocates   of   the   wave   theory   of   light   naturally 


Vision    and    Light  15 

supposed  that  in  light-waves  the  method  of  vibration  was  similar 
to  that  of  sound-waves,  and  since  certain  phenomena  could  not 
be  explained  under  such  conditions,  the  wave  theory  was  aban- 
doned for  a  century  and  a  half,  to  be  again  brought  into  promi- 
nence by  Fresnal  (1815),  who  introduced  the  assumption  that 
the  vibratory  motion  in  light-waves  was  transverse  to  the  direc- 
tion of  wave  motion.  With  this  modification,  all  the  observed 
phenomena  of  light  are  explainable.  But  this  assumption  cannot 
be  accepted  as  excluding  longitudinal  vibrations,  for  a  spherical 
wave  can  advance  only  in  the  directions  in  which  vibratory  dis- 
turbance is  taking  place.  We  must  conclude,  therefore,  that  light 
advances  by  means  of  longitudinal  disturbances  upon  which  is 
superposed  a  transverse  disturbance,  and  that  to  the  latter  are  due 
certain  characteristic  phenomena  which  are  explainable  only  by 
means  of  such  vibrations. 

The  exact  nature  of  the  vibratory  disturbances  which  give 
rise  to  light  is  unknown ;  it  was  formerly  supposed  that  there 
was  a  to-and-fro  movement  of  the  particles  of  the  conductor 
(ether),  just  as  there  is  in  sound-waves,  but  our  conception  of 
waves  has  been  greatly  broadened  by  the  introduction  by  Maxwell 
of  the  electro-magnetic  theory  of  wave  conduction.  In  the  trans- 
mission of  electricity,  a  certain  unknown  change  (polarization) 
takes  place  in  the  particles  of  the  conductor.  These  particles 
become  charged  with  energy,  which  they  transmit  to  the  ad- 
joining particles  and  so  on.  Each  particle,  having  transmitted 
its  energy,  returns  to  its  original  state  and  is  again  charged  by 
particles  behind  it,  and  so  the  process  continues.  Since  these 
changes  occur  in  rhythmical  impulses  or  pulsations,  they  con- 
stitute waves.  Doubtless  the  transmission  of  light  is  similar  to 
that  of  electricity — in  fact,  it  is  practically  certain  that  light 
differs  from  electricity  only  in  the  shorter  wave-length  and  more 
rapid  vibration  of  the  former. 

Recent  experiments  in  electricity  have  led  Professor  Thomson, 
of  Cambridge,  to  return  to  the  propulsion  theory  in  a  modified 
form.  Whatever  may  be  the  nature  of  the  corpuscles  or  electrons 
demonstrated  by  Professor  Thomson,  their  existence  is  insuffi- 
cient evidence  for  denying  the  theory  of  rhythmical  impulses 
(waves)  of  electricity  and  light— a  theory  which  has  hitherto 
been  found  indispensable  in  the  explanation  of  many  phenomena. 

As  with  the  ear,  only  waves  within  certain  limits  are  pro- 


16  Principles    of    Optics 

ductive  of  sound,  so  also  the  constitution  of  the  eye  is  such  that 
waves  within  certain  limits  of  periodicity  excite  vision,  while 
similar  waves,  whose  oscillatory  period  is  not  within  these  limits, 
do  not  produce  this  sensation. 

Color. — It  can  be  shown  with  the  aid  of  a  prism,  which 
causes  a  separation  of  waves  according  to  their  period  of  oscilla- 
tion, that  sunlight  is  composed  of  a  number  of  waves  of  varying 
periodicity  and  wave-length  (the  latter  being  inversely  proportional 
to  the  former),  and  that  other  waves  also  accompany  the  various 
waves  of  light.  Certain  waves  whose  vibratory  period  is  toe 
rapid  to  affect  the  retina  as  light  manifest  themselves  by  their 
power  of  causing  chemical  action;  while  others,  whose  vibratory 
period  is  too  slow  to  affect  the  retina  as  light,  are  manifested 
as  heat. 

The  various  colors  which  we  are  able  to  distinguish  depend 
upon  this  variation  of  vibratory  period.  While  a  number  of 
theories  have  been  put  forward  in  explanation  of  color  sensation, 
the  scheme  propounded  by  the  great  physicist,  Dr.  Thomas  Young 
(1801),  and  afterward  elaborated  by  Hclmholts  is  the  most 
satisfactory.  According  to  this  theory  the  various  light-waves 
are  divided  into  three  groups:  (1)  Those  of  least,  (2)  those  of 
intermediate  and  (3)  those  of  greatest  rapidity  of  vibration. 
Each  of  these  groups  of  waves  has  its  distinctive  action  upon 
the  retina.  Waves  comprised  in  the  first  group  cause  the  color 
red  to  be  seen;  those  in  the  second  group  are  productive  of  green, 
and  those  in  the  third,  or  most  rapid  group,  give  rise  to  the 
sensation  of  blue  (violet).*  These  three,  red,  green  and  blue,  are 
the  three  primary  colors — not  because  there  are  only  three  sets 
of  waves  (the  division  of  light  into  these  groups  being,  of  course, 
arbitrary),  but'because  of  the  limitations  of  the  eye. 

So  far  this  hypothesis  accords  well  with  the  phenomena  of 
color  vision,  but  in  the  further  endeavor  to  explain  how  these 
three  groups  of  waves  act  differently  upon  the  retina  serious 
difficulties  are  encountered.  It  is  assumed  that  there  are  three 
sets  of  terminal  elements,  one  set  for  each  group  of  waves,  and 
that  each  set  contains  a  characteristic  photo-chemical  substance 
which  is  affected  predominantly  by  the  group  of  waves  to  which 
it  is  adapted,  while  the  other  waves  affect  this  substance  in   a 

♦Opinions  differ  as  10  whether  blue  or  violet  should  be  regarded  as  the  primary  color. 


Vision   and   Light  17 

minor  degree  only.  Many  arguments  have  been  advanced  against 
this  assumption,  but  it  remains  more  plausible  than  any  of  the 
other  hypotheses  which  have  been  offered. 

Our  color  perception,  however,  is  not  limited  to  these  three 
elementary  sensations,  for  by  the  simultaneous  stimulation  in  vary- 
ing proportions  of  the  three  sets  of  elements  other  color  sensations 
are  afforded.  When  a  screen  is  placed  so  as  to  intercept  in  a 
darkened  room  a  beam  of  sunlight  which  has  passed  through  a 
prism  an  observer  may  count  on  the  screen  six  colors,  clearly 
distinct,  but  merging  gradually  into  the  contiguous  colors.  These 
six  colors  are  called  the  colors  of  the  spectrum.  They  are  red, 
orange,  yellow,  green,  blue,  and  violet.  To  these  Nezvton  added 
a  seventh  color,  indigo,  between  blue  and  violet. 

Orange  and  yellow,  lying  between  red  and  green,  result  from 
stimulation  of  the  retina,  in  proper  proportion,  by  the  waves  which 
give  rise  to  the  sensation  of  red  together  with  those  which  give 
rise  to  green,  but  with  little  or  no  stimulation  by  the  violet-pro- 
ducing waves,  the  latter  waves  having  been  eliminated  in  some 
way  from  the  light  which  enters  the  eye.  On  the  other  hand  the 
variations  of  color  as  seen  in  the  spectrum  lying  between 
green  and  violet  are  the  result  of  stimulation  of  the  retina  by 
those  waves  which  produce  green,  together  with  those  which 
produce  violet,  but  with  little  or  no  stimulation  by  the  red-produc- 
ing waves.  When  all  three  groups  of  waves  simultaneously 
stimulate  the  retina  and  without  predominance  of  any  one  group, 
xvhiteness  results. 

One  must  not  infer,  however,  from  the  foregoing  brief  de- 
scription of  the  Y oung-Hehnholtz  theory  of  color  perception  that 
there  is  a  sharp  border  line  between  the  three  groups  of  waves 
which  form  the  visible  spectrum.  For'  instance,  those  waves  of 
the  second  (intermediate)  group  which  approximate  in  periodicity 
the  first  group  (red  waves)  must  act  partly  as  red-producing 
waves ;  and  similarly  those  waves  which  approximate  the  blue- 
producing  waves  must  to  some  extent  give  rise  to  the  sensation 
of  blue. 

We  see,  therefore,  that  the  complete  spectrum  is  formed 
by  a  multiplicity  of  waves,  whose  rapidity  of  vibration  gradually 
increases,  beginning  with  the  ultra-red  and  extending  through  the 
visible  spectrum  to  the  chemical  waves  beyond  the  violet  margin. 
In  the  visible  part  of  the  solar  spectrum  there  are  seen  at  various 


18  Principles    of    Optics 

intervals  gaps  or  black  lines  (Fraunhofer  lines)  which  show  that 
certain  waves  have  been  destroyed.  The  discovery  of  these  lines 
has  led  to  the  important  study  of  spectrum  analysis,  for  it  has  been 
learned  that  the  absence  (absorption)  of  certain  waves  is  charac- 
teristic of  the  gaseous  substances  through  which  light  has  passed, 
and  that  from  the  number  and  position  of  such  lines  the  chemical 
composition  of  these  substances  can  be  determined. 

Velocity  of  Light,  Wave  Length,  Vibratory  Period. — 
It  has  been  found  from  astronomical  calculations  and  also  from 
terrestrial  experiments,  that  light  travels  through  air  and  through 
space  at  the  rate  of  300,000,000  meters  (approximately)  or 
186,000  miles  a  second. 

The  wave  length  at  various  parts  of  the  spectrum  has  also 
been  determined  by  very  delicate  experiments.  The  length  of 
the  red  wave,  near  the  beginning  of  the  visible  spectrum,  is  about 
ttst  mm>  and  f°r  violet,  near  the  terminus,  the  wave  length  is 
about  tj-jVit  mm-  Hence,  the  wave  length  for  light  is  embraced 
within  these  limits.  Since  light  travels  through  space  at  the  rate 
of  300,000,000,000  mm  a  second,  it  is  apparent  that  for  the  first 
wave  length  there  must  be  390  million-millions  of  these  wave 
lengths  or  vibrations  in  a  second,  and  for  the  last,  750  million- 
millions  of  vibrations  a  second. 

Luminosity. — By  this  term  we  denote  the  intensity  of  the 
sensation  which  results  from  retinal  stimulation.  Yellow  is  the 
color  of  greatest  intensity.  The  sensation  of  brightness  or  of  light 
seems  to  be  in  a  measure  independent  of  color,  for  when  the 
illumination  is  very  feeble,  one  may  be  able  to  detect  light  and 
yet  be  unable  to  assign  to  it  any  color.  Similarly  when  the 
illumination  is  very  powerful  no  distinction  of  color  can  be  made. 
This  is  explained  in  the  Y oung-H elmholts  hypothesis  by  assum- 
ing that  in  the  former  case  there  is  not  sufficient  excess  of 
stimulation  of  any  one  group  of  elements  to  make  its  color 
predominate,  and  in  the  latter  case  by  assuming  that  all  three 
sets  of  elements  are  so  greatly  stimulated  that  whiteness  results. 

Wave  Front. — A  luminous  point  emits  light  in  all  directions. 
If  the  rate  of  motion  is  the  same  in  all  directions,  the  wave  front 
will  evidently  be  spherical.  In  any  meridian,  as  in  the  plane  of 
the  paper  in  diagrammatic  representations,  the  wave  front  will  be 
represented  by  a  circle  (Fig.  1). 

It  is  a  matter  of  common  observation  that  light  travels  in 


Vision   and   Light 


19 


homogeneous  media  in  straight  lines — that  is,  it  does  not  bend 
around  corners  as  sound  does.  This  fact  was  formerly  thought 
to  be  inconsistent  with  the  wave  theory,  but  it  has  been  proved 
that  the  bending  must  diminish  with  the  diminution  of  the  wave 
length.  As  compared  with  sound  waves,  the  length  of  light  waves 
is  almost  infinitesimal  and,  consequently,  the  bending  of  light 
waves  must  be  ordinarily  inappreciable;  but  it  can  be  proved 


fig.  1 

experimentally  that  light  bends  around  corners  to  an  extent  com- 
mensurate with  its  wave  length.  The  shadow  cast  by  a  wire 
placed  in  the  path  of  light  is  less  than  the  actual  geometrical 
shadow,  which  shows  that  the  light  has  to  a  slight  extent  curved 
around  the  borders  of  the  wire.  The  study  of  this  phenomenon, 
called  diffraction,  constitutes  an  important  branch  of  optics. 

We  see  by  inspection  of   Fig.  2   that  the  nearer  the  eye 
is  to  the  source  of  illumination  the  greater  is  the  portion  of  the 


FIG.    2 


wave  which  will  enter  the  eye.  Hence,  the  luminosity  diminishes 
with  the  increase  of  distance  of  the  luminous  body.  It  is  also 
apparent  that  the  curvature  of  the  wave  front  diminishes  with  the 
increase  of  distance.  When  the  radius  O  A  is  so  great  that  the 
portion  of  the  wave  A  A  may. be  regarded  as  a  straight  line,  the 
wave  is  said  to  be  plane. 

Pencils  and  Rays. — A  small  portion  of  a  wave,  such  as  is 
represented  in  the  section  B  O  B  ( Fig.  1 )  is  called  a  pencil.    An 


20  Principles    of    Optics 

infinitesimal  pencil  is  called  a  ray.  The  lines  O  A  and  O  E 
(Fig.  2)  represent  rays.  A  ray  of  light  is  therefore  represented 
by  a  straight  line  perpendicular  to  the  wave  front. 

A  pencil  which  proceeds  from  a  point,  as  from  the  center  0, 
or  which  is  directed  towards  a  point,  is  said  to  be  homocentric. 
We  shall  learn  later  in  our  studies  that  owing  to  certain  disturb- 
ing factors,  pencils  may  lose  their  homocentric  character. 

Superposition  of  Waves. — We  do  not  ordinarily  have  to 
deal  with  mere  points  of  light,  but  with  objects  of  appreciable 
size.  Spherical  waves  proceed  from  every  point  of  a  luminous 
object.  Hence,  we  must  infer  that  many  waves  may  traverse  the 
same  space  at  the  same  time  without  destroying  one  another. 
This  is  known  as  the  principle  of  superposition;  it  has  its  analogue 
in  the  superposition  of  motions.  An  object  acted  upon  simultane- 
ously by  two  forces  will  be  displaced  by  each  force  as  if  the  other 
had  not  acted,  and  the  resultant  displacement  will  be  the  same 
as  if  the  object  had  first  been  displaced  by  one  and  subsequently 
by  the  other  force.  Just  as  it  is  possible  that  these  two  forces 
may  act  in  opposition  so  as  to  neutralize  each  other,  so  is  it 
possible  that  light-waves  of  a  certain  length  (color)  may  be 
destroyed  by  other  waves  of  the  same  length  acting  in  opposition 
to  the  first.  In  this  way  (by  the  destruction  of  certain  waves) 
objects  assume  their  characteristic  color,  although  illuminated  by 
sunlight,  which  contains  all  the  colors.  It  is  by  the  production  of 
an  experimental  interference  of  light-waves  that  the  wave-lengths 
for  the  different  Colors  have  been  determined. 

Formation  of  Images. — In  order  that  objects  may  be  seen, 
it  is  necessary  that  images  of  these  objects  shall  be  depicted 
upon  the  retina.  For  the  formation  of  an  image  it  is  essential 
that  light  from  any  point  of  the  object  shall  reach  a  correspond- 
ing point  on  the  intercepting  screen,  and  that  light  from  all 
other  parts  of  the  object  shall  be  excluded  from  this  point. 

A  very  simple  way  of  accomplishing  this  result  is  illustrated 
in  Fig.  3,  in  which  S.S  represents  an  opaque  diaphragm  having 
a  small  aperture  at  O.  Light  from  A  passes  through  the  aperture 
and  falls  upon  the  screen  at  Ax.  Light  from  other  parts  of  A  B 
cannot  reach  Alt  and,  therefore,  the  luminous  point  A  is  repro- 
duced at  A1.  Similarly  Bx  is  a  reproduction  of  B,  and  likewise 
the  intermediate  points  of  A1  B1  are  reproductions  of  the  cor- 
responding points  of  A  B,  and  A1  Bx  is  an  inverted  image  of  A  B. 


Vision    and    Light 


21 


Since  only  a  very  minute  pencil  of  light  can  be  allowed  to 
pass  through  the  aperture  in  the  diaphragm  without  blurring  of 
the  image,  the  illumination  of  the  image  is  comparatively  feeble, 
but  there  is  another  way  by  which  a  considerably  larger  pencil 
can  be  utilized  to  illuminate  the  image.  It  is  by  what  is  known 
as  refraction. 

s 


FIG.   3 


The  phenomenon  of  refraction  is  utilized  by  Nature  in  the 
production  of  vision,  and  the  eye  is  constructed  in  conformity 
with  the  laws  of  refraction.  To  this  branch  of  optics,, therefore, 
we  must  chiefly  devote  our  attention  in  the  following  chapters. 


The  following  authorities  have  been  consulted  in  the  prepara- 
tion of  the  foregoing  chapter : 

Gage,  Elements  of  Physics. 

Ganot,  Physics. 

Fresnal,  Theorie  de  la  Lumiere. 

Huy gtns,Tractatus  de  Lumine. 

Maxwell,  Electricity  and  Magnetism. 

Preston,  Theory  of  Light. 

Thomson,  J.  J.,  Electricity  and  Matter. 

Newton,  Opticks. 

Helmholtz,  Optique  Physiologique. 

Tscherning,  Physiologic  Optics. 

Mills,  Psychology  of  the  Visual  Act,  Posey  and  Spillers  Eye 
and  Nervous  System. 

Thomson  and  Weiland,  Normal  Color  Perception,  Norris  and 
Oliver's  System  of  Diseases  of  the  Eye. 

Young,  Theory  of  Light  and  Colors. 


CHAPTER  II 


THE  LAWS  OF  REFRACTION  AND  REFLECTION;  RE- 
FRACTION AND  REFLECTION  AT  PLANE 

SURFACES 

A  transparent  substance — a  substance  which  freely  permits 
the  passage  of  light  through  it — is  called  a  medium. 

A  substance  which  does  not  permit  the  passage  of  light 
through  it  is  said  to  be  opaque. 

When  light,  traversing  one  medium,  meets  another  of  differ- 
ent density  some  of  the  light  is  transmitted  to  the  second  medium 
and  some  of  it  continues,  with  its  direction  changed,  in  the  first 
medium. 

When  the  second  medium  offers  some  resistance  to  the 
passage  of  light,  a  certain  portion  of  the  incident  wave  is  con- 
verted into  some  other  form  of  energy.  The  part  of  the  light 
energy  so  transformed,  being  lost  as  light,  is  said  to  be  absorbed. 

Many  substances  which,  in  thin  layers,  are  transparent,  offer 
such  resistance  to  the  passage  of  light  that  only  a  small  part  of 
an  incident  wave  can  pass  through  thick  strata  of  these  substances. 
On  the  other  hand,  a  substance  which  under  ordinary  circum- 
stances appears  to  be  opaque,  may  not  be  entirely  so  when  placed 
in  the  path  of  light  of  great  intensity. 

A  substance  which  permits  the  passage  of  some  light,  but  in 
such  a  diffused  condition  that  objects  cannot  be  seen  through  it 
is  said  to  be  translucent. 

The  difference  between  a  transparent  and  an  opaque  body 
lies  in  the  structural  peculiarity  of  the  substance.  A  common 
illustration  of  this  difference  is  afforded  by  ice  or  glass,  each  of 
which  is  transparent  in  (thin)  homogeneous  layers  but  is  opaque 
in  a  crushed  or  pulverized  condition.  The  opacity  in  the  latter 
state  is  due  to  the  presence  of  air  between  the  particles  of  denser 

(22) 


Refraction    and    Reflection  23 

material.  Because  of  the  resulting  heterogeneity  of  the  structure 
the  wave  is  so  disturbed  by  reflection  at  each  of  the  many  surfaces 
that  its  penetrating  power  is  lost. 

The  Law  of  Refraction. — Of  the  two  chief  portions  of  an 
incident  wave  let  us  first  turn  our  attention  to  that  portion  which 
passes  into  the  second  medium.  We  learn  from  common  observa- 
tion that  objects  undergo  an  apparent  displacement  when  we 
view  them  lying  in  a  body  of  water.  This  displacement  results 
from  a  change  in  the  course  of  the  rays  which  takes  place  at 
the  surface  of  the  water.  This  change  of  direction  is  called 
refraction  (from  refr anger e,  to  break),  because  the  path  of  the 
rays  is  broken  or  altered. 

Refraction  is.  therefore  the  change  of  direction  zvhich  rays  of 
light  undergo  when  they  pass  from  one  medium  to  another 
of  different  density. 

WiUebrod  Snell,  of  Leyden,  is  accredited  as  the  discoverer  of 
the  law  of  refraction  (1621).  He  did  not,  however,  publish  the 
result  of  his  researches,  and  as  this  law  was  more  fully  explained 
by  Dcs-Cartes  (1637),  it  is  often  called  by  his  name.  It  was 
Des-Cartes  who  first  formulated  it  in  the  terms  commonly  used, 
as  follows:  The  incident  ray,  the  refracted  ray,  and  the  normal 
(perpendicular)  to  the  surface  lie  in  a  common  plane ;  the  inci- 
dent and  the  refracted  ray  lie  on  opposite  sides  of  the  normal; 
and  the  sine  of  the  angle  of  incidence  bears  a  constant  ratio  to 
the  sine  of  the  angle  of  refraction. 

The  angle  of  incidence  is  the  angle  which  the  incident  ray 
makes  with  the  normal  to  the  surface  (N S  R)  and  the  angle  of 
refraction  is  the  angle  which  the  refracted  ray  makes  with  the 
normal  (N1  S  RJ   (Fig.  4). 

If  we  denote  the  angles  of  incidence  and  refraction  by  i  and  r 

respectively,  the  law  of  refraction  is  expressed  by  the  equation 

sin   i 

=  n. 

>in  r 

The  constant  ratio  n  is  called  the  refractive  index.'* 

Snell  deduced  this  law  by  recording  the  results  of  many  ex- 
periments. He  knew  nothing  of  the  wave  theory  of  light,  of 
which  the  law  of  refraction  is  a  necessary  sequence,  for  the  con- 
stant n  represents  the  relative  velocity  of  light  in  the  two  media, 

*  Wo  shall  subsequently  learn  that  the  refractive  index  varies  with  the  color  of  the  light. 
Unless  it  is  otherwise  specified,  the  refractive  index  refers  to  the  average  index,  or  that  for 
yellow  light. 


24 


Principles    of    Optics 


the  velocity  being  less  as  the  density  is  greater.  The  refractive 
index  has  been  determined  for  various  substances  with  reference 
to  air,  the  index  of  the  latter  being  regarded  as  unity. 

The  indices  of  the  substances  with  which  we  are  chiefly  con- 


The  diagram  of  Des-Cartes  illustrating  the  law  of  refraction.      The  sine  of  the  angle   of 
I)  B  EC 

incidence  is  expressed    by  ~rr^- ',  the  sine  of  the  angle  of    refraction   by  .     Since 

o  b  a  c 

S  B  =■  S  C,  D  B  bears  a  constant  ratio  to  E  C. 

cerned  are  as  follows:  Water,  1.33;  glass,  from  1.5  to  1.7; 
cornea,  1.377;  aqueous  and  vitreous  humors  of  the  eye,  1.337; 
crystalline  lens,  1.437  (approximately).  The  denser  the  substance 
the  higher  is  the  index,  as  a  rule. 

If  the  indices  of  two  media  with  reference  to  air  are  denoted 
by  11,  and  nlt  respectively,  the  index   for  the  two  media  with 

reference  to  each  other  is  expressed  by   --1    and  the  formula  of 

refraction  becomes 


n 


Sill     I 

sili  r 


"1 
n 


The  sine  of  an  angle  increases  with  the  angle,  and  therefore 
when  »x  is  greater  than  n  the  angle  of  incidence  (N  S  R)  is 
greater  than  the  angle  of  refraction  (N1  S  R,_).  This  must  be  so 
in  order  to  preserve  the  constant  ratio  in  the  foregoing  equation. 

Similarly,  if  nx  is  less  than  n  the  angle  of  incidence  must  be 
less  than  the  angle  of  refraction. 

We  have  therefore  the  following  rule:  When  light  passes 
from  a  rarer  to  a  denser  medium  the  rays  are  deflected  towards 
the  normal  to  the  surface,  and  when  it  passes  from  a  denser  to  a 
rarer  medium  the  rays  are  deflected  away  from  the  normal.    The 


Refraction   and   Reflection  25 

formula  for  refraction  also  shows  that  the  deviation  of  a  ray  in- 
creases or  diminishes  as  the  angle  of  incidence  increases  or 
diminishes,  for  the  sine  of  an  angle  increases  less  rapidly  than 
the  angle,  and  the  more  so  according  as  the  angle  is  greater. 

Therefore   in   order  to  maintain   the   constant  ratio    —       the 

n  ' 

greater  angle  (whether  this  is  the  angle  of  incidence  or  refrac- 
tion) must  increase  more  rapidly  than  the  smaller  angle.  Conse- 
quently the  difference  between  these  two  angles  (which  represents 
the  deviation  of  the  ray)  must  increase  with  an  increase  of  the 
angle  of  incidence. 

This  brings  us  to  the  consideration  of  the  ray  which  meets 
the  surface  perpendicularly.  In  this  case,  in  which  the  angle  of 
incidence  is  zero,  the  angle  of  refraction  must  likewise  be  zero. 
Therefore,  the  ray  which  meets  the  surface  perpendicularly 
undergoes  110  refraction. 

Passage  of  Light  through  a  Medium  bounded  by  Two 
Parallel  Surfaces. — Rays  of  light  passing  through  such  a  body 
and  reentering  the  first  medium,  undergo  no  change  of  direction. 
This  is  illustrated  in  Fig.  5,  in  which  .£  R  represents  a  ray  passing 


fig.  5 

through  the  medium  M  N.  Since  the  two  refracting  surfaces  are 
parallel,  the  normals  at  A  and  D  are  parallel.  The  angle  of  re- 
fraction at  the  first  surface  must  therefore  be  equal  to  the 
angle  of  incidence  in  the  second  refraction,  and  consequently 
the  second  angle  of  refraction  is  equal  to  the  first  angle  of 
incidence.  In  other  words,  the  two  deviations  exactly  neutralize 
each  other,  and  there  is  no  change  of  direction  of  the  ray;  but 
there  is  a  lateral  displacement  of  every  ray  except  that  which  is 
perpendicular  to  the  surfaces. 

Prisms 

A  prism  is  a  wedge-shaped  portion  of  material  bounded  by 
two  plane  surfaces  meeting  in   an   edge.     The  angle   included 


26 


Principles    of    Optics 


by  these  two  faces  is  called  (in  optics)  the  refracting  angle. 
A  plane  which  is  perpendicular  to  the  edge,  and  consequently 
to  each  face  of  the  prism,  is  called  a  principal  plane  of  the  prism. 
At  right  angles  to  any  principal  plane — that  is,  in  the  direction 
of  the  edge  of  the  prism — the  two  faces  are  parallel  to  each 
other. 

Refraction  of  Parallel  Rays  by  a  Prism. — A  ray  of  light 
passing  through  a  prism  whose  refractive  index  is  greater  than 


fig.  6 


that  of  the  surrounding  medium  will  always  be  deviated  away 
from  the  apex  or  edge  of  the  prism.  In  Fig.  6  B  A  C  represents 
a  principal  section  or  plane  of  a  prism,  and  0  R  represents  any 
one  of  a  series  of  parallel  rays  passing  through  the  prism  in  this 
plane.  At  the  first  surface  the  rays,  on  entering  the  dense 
medium,  are  refracted  towards  the  normal  to  this  surface,  and 
at  the  second  surface,  on  re-entering  the  rarer  medium,  the 
rays  are  refracted  away  from  the  normal  to  the  surface.  The 
effect  in  each  instance,  in  our  illustration,  is  a  deviation  away 
from  the  apex  of  the  prism.  This,  however,  is  not  always  the 
case.  The  rays  may  meet  the  first  surface  perpendicularly,  or 
they  may  emerge  at  the  second  surface  perpendicularly,  or  they 
may  even  be  bent  towards  the  apex  at  one  or  the  other  surface. 
In  the  last  case  it  must  be  proved  that  the  refraction  towards 
the  apex  is  less  than  the  opposite  refraction  at  the  other  surface. 
The  student  who  is  at  all  familiar  with  geometry  will  have  no 
difficulty  in  satisfying  himself  that  this  is  so,  for  he  will  readily 
see  that  the  angles  of  incidence  and  refraction  are  greater  at 
that  surface  at  which  the  refraction  is  away  from  the  apex  than 
at  the  other  surface.     We  have  already  learned  that  the  greater 


Refraction    and    Reflection  27 

deviation  occurs  at  the  surface  where  the  angle  of  incidence 
is  greater. 

As  the  incident  rays  are  parallel,  the  angles  of  incidence 
and  refraction  must  be  the  same  for  all  the  rays,  and  conse- 
quently the  rays  will  still  be  parallel  after  passing  through  the 
prism. 

Since  the  prism  deviates  light  away  from  the  apex,  the  ap- 
parent position  of  an  object  as  seen  through  a  prism  is  displaced 
towards  the  apex  (Fig.  7). 

Minimum  Deviation. — It  was  first  shown  by  Sir  Isaac 
Newton  that  the  deviation  of  a  ray  of  light  is  less  when  it  passes 
through  a  prism  symmetrically,  the  angles  of  incidence  and 
emergence  being  equal,  as  in  Fig.  7,  than  in  any  other  position 
of  the  ray,  and  that  the  deviation  increases  at  a  continually 
increasing  rate  as  the  ray  departs  from  this  position. 

When  the  prism:  is  of  glass  whose  index  is  about  1.5  the 
deviation  of  the  symmetrical  ray  is  very  nearly  equal  to  one-half 
of  the  refracting  angle  of  the  prism,  as  long  as  this  angle  does 
not  exceed  eight  or  ten  degrees.  For  greater  angles  the  deviation 
is  relatively  more.  The  formula  expressing  the  deviation  of  a  ray 
by  a  prism  is  given  in  the  appendix. 

Refraction  of  a  Spherical  Wave  (Divergent  Rays)  by 
a  Prism. — When  light  enters  a  prism  diverging  from  a  point 


fig.  7 

near  the  prism  the  angles  of  incidence  of  the  various  rays  will 
differ  one  from  another,  and  the  study  of  this  condition  of 
refraction  is  much  more  complicated  than  that  in  which  we  may 
regard  all  the  rays  as  being  parallel.  We  need  not,  however, 
enter  into  a  discussion  of  this  subject,  for  in  our  use  of  prisms 
in  ophthalmology  we  make  the  assumption  that  all  rays  are 
equally  deviated,  and  we  do  this  without  material  error.     But  it 


28  Principles    of    Optics 

is  because  of  this  unequal  refraction  of  the  various  rays  that 
objects  appear  distorted  when  seen  through  strong  prisms,  or 
even  through  weaker  prisms  if  the  rays  coming  from  the  objects 
are  far  removed  from  the  symmetrical  position.  Not  only  is 
there  under  such  conditions  an  unequal  deviation  of  the  rays 
from  different  parts  of  an  object,  but  also  of  the  differently 
inclined  rays  of  each  pencil,  so  that  the  rays  which  are  homo- 
centric  before  entering  the  prism  will  not  remain  so  after 
passing  through  the  prism.  This  will  be  briefly  explained  when 
we  reach  the  subject  of  asymmetrical  refraction. 

Dispersion  of  Colors. — We  have  already  learned  that 
prisms  have  the  power  of  separating  light  into  its  various 
colors.  This  separation  or  dispersion  of  colors  is  due  to  the 
fact  that  the  degree  of  retardation  effected  by  a  dense  medium 
varies  with  the  wave  length.  The  shorter  the  wave  length  the 
greater  is  the  retardation  and,  consequently,  the  deviation.  As 
violet  is  the  color  of  least  wave  length,  the  deviation  is  greatest 
for  this  color;  while  red,  being  the  color  of  greatest  wave  length, 
is  the  color  which  undergoes  the  least  deviation  in  passing 
through  the  prism. 

In  order  to  obtain  a  colored  spectrum  we  must  exclude  all 
light  except  a  narrow  beam,  for  otherwise  the  waves  which  pass 
through  various  parts  of  the  prism  overlap  and  form  the  com- 
pound light,  and  only  that  part  of  the  light  which  passes  along 
the  borders  of  the  prism  is  tinged  with  color.  The  apex  border 
will  be  tinged  with  violet,  since  this  color  is  deviated  farther 
towards  the  apex  than  any  other  color;  so  the  base  border  will 
be  tinged  with  red,  since  this  color  undergoes  less  deviation  than 
any  other  color. 

Numeration  of  Prisms. — There  are  several  methods  of 
measuring  the  strength  or  deviating  power  of  prisms.  The 
method  which  was  formerly  used  altogether  in  ophthalmology 
consists  in  numbering  the  prism  in  terms  of  its  refracting  angle 
(Pr.  i°,  2°,  30,  etc.).  The  theoretical  disadvantages  of  this 
method  are  obvious,  since  no  consideration  is  given  to  the  refrac- 
tive index  of  the  material  of  which  the  prism  is  made. 

The  first  improvement  in  prism  notation  was  made  as  a 
result  of  the  discussion  of  this  subject  by  members  of  the 
Ophthalmological  Congress  held  in  Washington  in  1887.  In 
the  method  proposed  at  this  Congress  the  prism  is  numbered  in 


Refraction    and    Reflection  29 

terms  of  the  minimum  deviating  power  (Pr.  id,  2d,  etc.).  We 
have  learned  that  in  weak  prisms  the  minimum  deviating  power 
is  about  one-half  of  the  refracting  angle.  A  prism  of  2d  is 
therefore  equivalent  to  a  prism  of  40,  as  measured  by  the  refract- 
ing angle  system.  A  disadvantage  of  this  system  of  numbering 
prisms  in  the  degrees  of  minimum  deviation  is  the  liability  of 
its  confusion  with  the  first  system,  since  in  each  case  the  unit 
of  measure  is  the  degree. 

In  order  to  obviate  confusion  of  the  deviating  power  with 
the  refracting  angle,  and  at  the  same  time  to  introduce  the 
decimal  system  into  prism  notation  Dennett  proposed  the  centrad 
system.  In  this  the  minimum  deviation  is  measured  in  centrads, 
a  centrad  being  T^  of  the  radius  as  measured  on  the  cir- 
cumference. The  circumference  of  a  circle  being  measured  by 
3600,  and  the  radius  being  approximately  F.2W2  °f  the 
circumference,  it  follows  that  the  centrad  .  (y^g-  of  the  radius) 
is  34'  22" — slightly  more  than  one-half  of  a  degree. 

The  method,  however,  which  has  gained  most  favor  and 
which  has  already  come  into  quite  general  use  in  this  country 
is  the  prism  diopter  system.  This  system,  which  was  introduced 
by  Prentice  in  1890,  differs  from  the  centrad  system  chiefly  in 
that  the  prism  diopter  is  measured  on  a  straight  line,  while  the 
centrad  is  an  arc  of  a  circumference. 

A  prism  diopter  is  the  unit  represented  by  a  prism  which 
deviates  the  ray  of  perpendicular  incidence  (not  the  ray  of  mini- 
mum deviation)  ^1^  of  a  meter  (one  centimeter)  at  a  distance 
of  one  meter.  This  method  affords  a  very  easy  way  of  measuring 
the  strength  of  a  prism,  for  it  is  only  necessary  to  count  on  a 
metric  scale  the  number  of  centimeters  of  displacement  whicli 
a  line  undergoes  when  the  prism  is  placed  at  a  distance  of  one 
meter  from  the  scale.  If  there  are  2  cm  of  displacement  the 
strength  of  the  prism  is  2  prism  diopters ;  if  there  are  3  cm  of 
displacement  the  strength  is  3  prism  diopters,  etc.  The  prism 
diopter  has  been  adopted  by  the  principal  optical  manufacturers 
of  America,  who  make  all  their  prisms  in  accordance  with  this 
system  of  measurement.  The  character  (  )  is  commonly  used 
to  express  the  term  prism  diopter. 

The  following  table,  whose  method  of  derivation  may  be 
found  in  the  appendix,  gives  the  deviating  power  of  various 
prisms  as  numbered   in   terms  of  the  refracting  angle  and   the 


30  Principles    of    Optics 

prism  diopter.  In  estimating  the  deviating  power  of  the  prisms 
as  measured  by  the  refracting  angle  the  refractive  index  is 
regarded  as  1.52  and  the  incident  ray  is  perpendicular  to  the 
surface  of  the  prism,  as  it  is  in  the  prism  diopter  system. 


TABLE 

Refracting 
Angle 

Deviation 

Prism 
Diopter 

Deviation 

1° 

= 

3i' 

— 

12" 

IA 

= 

34'     —     22" 

3° 

= 

i° 

— 

33' 

— 

45" 

3^ 

= 

1° 

— 

43/ 

5° 

= 

2° 

— 

36' 

— 

2" 

5A 

= 

2° 

— 

52' 

7° 

— 

3° 

— 

40' 

— 

2" 

7A 

= 

4° 

9° 

= 

4° 

— 

45' 

— 

1" 

9A 

= 

5° 

— 

9' 

ii° 

= 

5° 

— 

52' 

IIA 

= 

6° 

— 

17' 

13° 

= 

6° 

— 

59< 

13A 

= 

7° 

— 

24/ 

15° 

= 

8° 

— 

10' 

I5A 

= 

8° 

— 

32/ 

2O0 

rzzr 

ii° 

— 

19' 

20A 

== 

ii° 

— 

19' 

From  the  foregoing  table  we  see  that  for  the  weaker  prisms 
the  prism  diopter  is  slightly  stronger  than  the  corresponding 
number  in  the  refracting  angle  series,  and  that  the  difference 
between  the  two  diminishes  as  the  strength  of  the  prism  in- 
creases, so  that  the  deviation  produced  by  a  prism  of  200  (re- 
fracting angle)  equals  the  deviation  of  a  prism  of  20  a  .  Beyond 
this  number  a  prism  as  measured  by  the  refracting  angle  is  of 
greater  deviating  power  than  the  corresponding  number  of 
the  prism  diopter  system. 

The  meter  angle  has  also  to  some  extent  been  used  as  a 
prism  unit.  Its  value  depends  upon  the  interocular  distance, 
which  is  a  variable  quantity,  and  therefore  this  unit  is  not  suitable 
for  numbering  prisms,  although,  as  we  shall  hereafter  learn,  it 
is  very  convenient  for  measuring  convergence. 

Combination  of  Prisms* — It  is  desirable  that  we  should 
know  how  to  determine  the  single  prism  which  is  equivalent  to 
two  specified  prisms  acting  in  different  directions.  We  can  very 
easily  determine  the  equivalent  prism  by  diagrammatic  construc- 
tion, as  is  illustrated  in  Fig.  8.  Let  us  suppose,  for  instance, 
that  we  have  a  prism  of  3  a  ,  which  deviates  light  to  the  right 


Refraction    and   Reflection  31 

in  the  horizontal  plane,  combined  with  a  prism  of  2  a,  which 
deviates  the  rays  vertically  upward.  Starting-  at  A  we  measure 
off  3  cm  to  the  right  in  the  horizontal  direction.  This  distance 
A  C  represents  the  deviating  power  of  the  first  prism.  We  next 
measure  off  CD  (2  cm)  in  the  vertical  direction,  which  represents 
the  deviating  effect  of  the  second  prism. 


fig.  8 

Therefore,  we  see  that  the  two  prisms  acting  together 
deviate  a  ray  from  A  to  D,  and  that  the  deviating  action  of  the 
single  equivalent  prism  is  represented  by  the  line  A  D.  We 
measure  this  line  and  find  its  length  is  about  3.6  cm,  and  conse- 
quently, if  the  prisms  are  numbered  in  prism  diopters  the 
equivalent  prism  will  have  a  strength  of  3.6  prism  diopters.  The 
direction  of  the  principal  plane  (the  base  apex  line)  of  the 
equivalent  prism  is  also  determined  by  the  line  A  D.  With  the 
aid  of  a  protractor  we  find  the  angle  D  AC  to  be  about  35  °, 
which  marks  the  position  of  the  equivalent  prism. 

This  diagram  serves  also  for  reversing  the  process — for 
replacing  a  single  prism  acting  in  an  intermediate  meridian  by 
two  prisms,  one  acting  vertically  and  the  other  horizontally. 

Reflection 

That  part  of  the  wave  of  light  which,  instead  of  entering 
the  second  substance,  glances  off  from  the  surface  and  continues 
to  travel  in  the  first  substance,  is  said  to  be  reflected. 

When  a  wave  of  light  is  incident  upon  a  surface  separating 
two  substances  the  proportion  which  is  reflected  depends  not 
only  upon  the  transparency  of  the  second  substance  and  upon 
its  power  of  absorbing  light,  but  also  upon  the  angle  at  which 
the  rays  meet  the  surface.     The  amount  of  light  which  enters 


32  Principles    of    Optics 

a  medium  diminishes,  while  the  amount  which  is  reflected  in- 
creases as  the  obliquity  of  the  rays  increases. 

It  is  by  reflection  that  non-luminous  objects  are  visible  to 
us,  and  it  is  by  means  of  the  unevenness  of  the  surfaces  that  we 
are  able  to  see  the  details  of  objects.  Light  reflected  in  this 
way  from  unpolished  surfaces  is  said  to  be  irregularly  reflected, 
or  diffused  or  scattered. 

On  the  other  hand,  the  light  which  is  reflected  from  polished 
surfaces  is  said  to  be  regularly  reflected.  By  such  reflection  we 
do  not  see  the  surface,  but  a  reproduced  image  of  the  luminous 
body  from  which  the  light  proceeds.  The  images  formed  by 
reflection  at  the  smooth  surfaces  of  the  cornea  and  crystalline 
lens  are  of  the  utmost  importance  in  ophthalmometry,  and  it  is 
chiefly  with  a  view  to  the  study  of  these  images  that  we  devote 
our  attention  here  to  the  phenomena  of  reflection. 

The  smoother  a  surface  is  the  greater  is  the  regular  re- 
flection and  the  less  is  the  diffused  light ;  but  even  in  highly 
polished  surfaces  there  is  usually  some  irregular  reflection  by 
which  the  surface  is  rendered  visible.  At  times,  however,  es- 
pecially when  the  illumination  is  weak,  the  presence  of  the  re- 
flecting mirror  may  altogether  escape  our  attention.  As  is  well 
known,  this  fact  is  sometimes  made  use  of  in  the  production  of 
theatrical  illusions. 

The  Law  of  Reflection. — We  have  learned  that  the  law 
of  refraction  was  first  discovered  experimentally  and  was  after- 
ward proved  mathematically  as  being  in  conformity  with  the 
wave  theory  of  light.  The  same  is  to  be  said  of  the  law 
of  reflection,  but  this  law,  being  more  apparent  upon  superficial 


fig.  9 

N S  I  (angle  of  incidence)  =  X S H  (angle  of  reflection). 

observation  than  the  law  of  refraction,  was  discovered  at  a  much 
earlier  date  than  the  latter.  The  law  of  reflection  was.  in  fact, 
known  to  the  ancients.  It  is  usually  expressed  in  the  following 
terms : 


Refraction    and    Reflection  33 

The  incident  and  the  reflected  ray  lie  in  a  common  plane  with 
the  normal  to  the  surface,  and  the  angle  of  incidence  (the  angle 
zvhich  the  incident  ray  makes  with  the  normal)  is  equal  to  the~> 
angle  of  reflection  (the  angle  which  the  reflected  ray  makes  with 
the  normal).    (Fig.  p.) 

Reflection  at  Plane  Surfaces. — When  the  reflecting  sur- 
face is  plane,  as  M  M  in  Fig.  10,  all  the  normals  to  the  surface 
are  parallel,  and  since  the  angles  of  incidence  and  reflection  are 


FIG.    10 


equal,  it  follows  from  the  geometrical  relations  that  the  point  /, 
which  is  the  image  of  0,  is  as  far  behind  the  surface  as  O  is 
in  front  of  it.  So  also  Iv  the  image  of  0lt  lies  as  far  behind  the 
mirror  as  Ox  lies  in  front  of  it. 

If  0  Ox  represents  an  object,  /  Ix  is  the  image  formed  by 
reflection  of  this  object.  The  object  and  its  image  are  of  equal 
size,  but  there  is  a  lateral  reversal  of  the  image  relatively  to  the 
object,  for  the  point  0  of  the  object  is  on  the  extreme  right, 
while  its  image  /  is  on  the  extreme  left. 

Since  the  rays  of  light  do  not  actually  emanate  from  the 
points  of  the  image  behind  the  reflecting  surface,  but  only  appear 
to  come  from  these  points,  these  points  constitute  a  virtual  image 
in  contradistinction  to  those  images  in  which  the  image  is  actually 
formed  by  the  meeting  of  the  rays.  Images  of  the  latter  kind 
are  called  real  images. 

Total  Reflection. — We  have  learned  that  as  the  obliquity 
of  rays  increases  the  reflected  portion  of  the  wave  increases  at 
the  expense  of  the  portion  which  enters  the  second  substance. 


34  Principles    of    Optics 

If  the  second  medium  is  denser  than  the  first  some  of  the  light 
will  always  enter  this  denser  medium  no  matter  how  great  the 
obliquity  of  the  rays  may  be ;  but  this  is  not  so  when  the  second 
medium  is  the  rarer  of  the  two,  for  when  the  rays  reach  a  certain 
degree  of  obliquity  none  of  the  light  passes  into  this  rarer  medium, 
the  entire  wave  being  reflected. 

The  reason  for  this  phenomenon  of  total  internal  reflection 
is  readily  understood  from  the  accompanying  illustration 
(Fig.  n).  When  the  obliquity  is  such  as  represented  by  the  ray 
OSR  the  corresponding  angle  of  refraction  is  ninety  degrees, 


FIG.    II 


and  a  ray  Ox  S  Rx  whose  obliquity  is  greater  than  that  of  O  S  R 
would  require  a  still  greater  angle  of  refraction,  but  as  the  angle 
of  refraction  cannot  be  greater  than  ninety  degrees,  we  have 
an  impossible  condition.  No  light  can  pass  out  of  the  dense 
medium  under  these  circumstances. 

The  angle  at  which  light  ceases  to  pass  out  of  a  dense 
medium  (the  critical  angle)  can  be  determined  by  experiment  or 
from  the  formula  of  refraction.  By  making  the  angle  of  re- 
fraction (r)  equal  to  ninety  degrees  in  this  equation  we  obtain 
the  corresponding  value  of  the  angle  of  incidence  as  expressed 
in  terms  of  the  sine  of  this  angle  and  the  refractive  index  (sin  i 
=  n).  If  we  know  the  refractive  index  we  can  ascertain  the 
value  of  the  limiting  angle  of  incidence  or  the  critical  angle 
from  a  table  of  sines.  On  the  other  hand  we  may  determine  the 
critical  angle  by  experiment  and  deduce  therefrom  the  refractive 
index. 

The  phenomenon  of  total  reflection  is  of  great  practical 
importance  in  the  construction  of  certain  optical  instruments,  for 
by  its  means  the  direction  of  rays  can  be  changed  with  very 
little  loss  of  light. 


Refraction    and    Reflection  35 

It  is  largely  to  this  phenomenon  also  that  the  diamond  and 
other  gems  owe  their  brilliancy.  Because  of  the  high  refractive 
index  the  critical  angle  is  small  and  much  of  the  light  which 
enters  the  gem  undergoes  total  reflection.  After  one  or  more 
reflections  the  rays,  meeting  a  surface  perpendicularly  or  nearly 
so,  pass  again  into  the  air,  and  may  thus  enter  the  eye  of  an 
observer. 

The  following  authorities  have  been  consulted  in  the  prep- 
aration of  the  foregoing  chapter : 

Des-Cartes,  Dioptrice. 

Newton,  Opticks. 

Gage,  Elements  of  Physics. 

Ganot,  Physics. 

Heath,  Geometrical  Optics. 

Preston,  Theory  of  Light. 

Jackson,  Designation  of  Prisms  by  the  Angle  of  Deviation, 
Report  of  Ninth  International  Congress,  1887. 

Dennett,  Prisms  and  Prismometry,  Norris  and  Oliver's  Sys- 
tem of  Diseases  of  the  Eye. 

Prentice,  A  Metric  System  of  Numbering  and  Measuring 
Prisms,  Archives  of  Ophthalmology,  1890. 


CHAPTER  III 


REFRACTION  AND  REFLECTION  AT  SPHERICAL 

SURFACES 

We  have  seen  that  an  image  of  an  object  can  be  projected 
on  a  screen  by  allowing  a  minute  pencil  of  light  to  pass  through 
a  pinhole  opening  in  ah  opaque  diaphragm,  but  that  owing  to  the 
small  amount  of  light  that  can  be  allowed  to  pass  through  the 
opening  without  blurring  of  the  image  the  illumination  of  the 
image  is  very  feeble.  Much  brighter  and  better  images  can  be 
obtained  by  refraction  at  suitably  curved  surfaces.  By  means  of 
a  spherical  surface  separating  two  media  of  different  density 
a  considerable  portion  (pencil)  of  the  rays  proceeding  from  a 
point  may  be  united  in  another  point  or  focus  after  refraction. 
The  means  by  which  this  takes  place  is  illustrated  in  Fig.   12, 


RARE 


DENSE 


FIG.    12 


in  which  S  A  S1  represents  a  section  of  a  convex  spherical  surface 
separating  two  media,  the  second  medium  (that  on  the  right) 
being  denser  than  the  first,  while  S  O  5\  represents  a  section  of  a 
pencil  of  light  proceeding  from  0*  That  portion  of  the  wave 
which  travels  along  0  A  encounters  the  denser  medium  sooner 
than  the  portions  which  travel  along  0  B  and  0  Bx.  We  have 
learned  that  the  progress  of  light  is  less  rapid  in  dense  than  in 
rare  media;  therefore  it  is  evident  that  while  the  peripheral  rays 

*A  refracting  or  reflecting  surface  is  convex  or  concave  according  as  the  convex  or  con- 
cave surface  is  turned  towards  the  incident  rays. 

(36) 


Refraction    and    Reflection 


37 


are  traveling  the  distance  BS  (or  BXS^  in  the  rarer  medium, 
the  medial  ray  travels  the  distance  A  H,  which  is  less  than  B  S 
or  B-l  Sv  Upon  the  entrance  of  the  entire  pencil  into  the  denser 
medium  we  see  that  S  H  S  represents  the  wave  front,  and  that 
S  I,  O  I,  and  5\  /,  represent  rays,  all  meeting  in  the  focus  /.  The 
ray  O  I,  which  is  perpendicular  to  the  refracting  surface,  and 
which  consequently  undergoes  no  deviation,  is  called  the  optic 
axis.    The  two  points  O  and  /  are  called  conjugate  foci. 

We  have  in  the  foregoing  illustration  assumed  without  proof 
that  the  wave  front  after  refraction,  5  H  Slt  is  spherical  in  form, 
and  that  all  the  rays  of  the  pencil  meet  in  a  point.  As  a  matter 
of  fact,  the  refracted  wave  front  is  not  mathematically  spherical, 


RARE 


DENSE 


FIG.    13 

yet  it  approximates  this  form  so  nearly  that  in  our  studies  we 
may  base  our  calculations  upon  the  assumption  that  (with  a  certain 
restriction  as  to  the  size  of  the  pencil)  all  the  rays  which  proceed 
from  a  point  O  can  be  united  in  a  focus  /  by  refraction  at  a 
spherical  surface. 

The  position  of  the  focus  /  depends  upon  the  following 
factors:  (1)  The  curvature  of  the  surface,  (2)  the  relative 
density  of  the  two  media  and   (3)  the  position  of  the  point  O. 

When  the  point  O  is  very  far  removed  from  the  refracting 
surface  the  divergence  of  the  rays  is  so  slight  that  we  may 
regard  them  as  being  practically  parallel.  When  we  speak  of 
parallel  rays  or  a  plane  wave,  therefore,  we  mean  either  that  the 
rays  emanate  from  a  distant  point  or  that  they  have  been 
rendered  parallel  by  a  previous  refraction.  In  either  case,  that 
is,  whether  the  rays  proceed  from  a  distant  point  or  whether  they 
are  actually  parallel  they  are  represented  diagrammatically  as  is 
illustrated  in  Fig.  13. 

Rays  which  are  parallel  before  refraction  at  the  convex 
surface  5"  5  are  brought  to  a  focus  at  F'.  This  point  is  called 
the  posterior  principal  focus.     When  the  point  of  origin  of  the 


38  Principles    of    Optics 

rays  is  at  a  point  F  (Fig.  14),  such  that  the  rays  are  parallel 
after  refraction,  the  conjugate  focus,  I,  is  infinitely  distant.  The 
point  F  is  called  the  anterior  principal  focus. 

If  the  point  0  is  nearer  to  the  surface  than  F  the  rays  will 
remain  divergent  after  refraction,  but  the  divergence  will  be 
less  than  it  was  before  refraction,  as  is  shown  in  Fig.  15.     The 


rays  which  proceed  from  0  will  not  be  united  in  a  real  focus, 
but  they  will  appear  to  proceed  from  the  virtual  focus  /. 

One  more  condition  remains  to  be  considered — that  in  which 
the  rays  of  light  have  been  rendered  convergent  by  a  previous 


i~--s:"~  >f  o- 


FIG.    15 

refraction  before  entering  the  denser  medium  at  the  convex 
surface.  This  condition  is  illustrated  in  Fig.  16,  in  which  the 
rays  are  converging  to  the  point  O,  and  this  convergence  being 
increased  by  the  refraction,  they  are  united  in  the  focus  /. 

We  must  bear  in  mind  in  this  connection,  however,  that  the  refrac- 
tion is  governed  by  the  law  that  the  rays  are  always  bent  towards  the 
normal  on  entering  the  denser  medium.  If  therefore  the  rays  are  so 
convergent  as  to  be  directed  towards  the  center  of  the  surface,  all  rays 
meet  the  surface  perpendicularly,  and,  consequently,  there  will  be  no 
refraction. 

If  the  convergence  of  the  rays  is  still  greater  so  that  they  are 
directed  to  a  point  on  the  optic  axis  nearer  than  the  center  of  the  sur- 
face, the  refraction  will  be  opposite  to  that  above  described — that  is,  the 
convergence  will  be  diminished. 


Refraction    and    Reflection 


39 


It  is  apparent  that  all  the  foregoing  diagrams,  illustrating 
refraction  at  a  convex  surface,  can  be  made  applicable  for 
illustrating  the  refraction  which  occurs  when  the  rays,  starting  in 
a  denser  medium,  pass  into  a  rarer  medium  at  a  concave  surface. 
In  Fig.  12,  for  instance,  rays  proceeding  from  /  in  the  dense 
medium  are  refracted  at  the  concave  surface  so  as  to  meet  at  O 
in  the  rarer  medium.  Similarly,  by  reversing  the  course  of  the 
rays  we  may  apply  the  other  diagrams,  and  we  see  that  the  effect 
of  refraction  by  a  convex  surface  when  the  first  medium  is  the 
rarer,  is  similar  to  that  by  a  concave  surface  when  the  first 
medium  is  the  denser. 

Summary  of  Collective  Refraction. — Since  in  all  the 
conditions    of    refraction    thus    far    illustrated    the    effect    is    an 


RARE 


DENSE 


r--j»  o 


FIG.    1 6 


increase  of  convergence  or  a  diminution  of  divergence, 
or  a  collecting  together  of  the  rays,  such  refraction  is  called 
collective. 

(i)  In  collective  refraction  the  two  principal  foci  are  real — 
that  is,  they  are  the  actual  meeting  points  of  rays  of  light. 

(2)  Rays  proceeding  from  a  point  will  be  brought  to  a 
real  focus  on  the  opposite  side  of  the  refracting  surface  as  long 
as  the  point  of  origin  is  farther  from,  the  surface  than  is  the 
anterior  principal  focus  (Fig.  12).  When  the  point  from  which 
the  rays  proceed  is  infinitely  distant — that  is,  when  we  may  regard 
the  rays  as  being  parallel,  they  meet  after  refraction  at  the 
posterior  principal  focus  (Fig.  13).  When  the  point  of  origin 
is  so  near  that  there  is  an  appreciable  divergence  of  the  rays, 
the  conjugate  focus  is  beyond  the  posterior  principal  focus,  as  in 
Fig.  12. 

(3)  Rays  proceeding  from  the  anterior  principal  focus  will 
be  parallel  after  refraction  (Fig.  14). 

(4)  Rays  proceeding  from  a  point  nearer  the  refracting  sur- 
face than  the  anterior  principal  focus  will  remain  divergent  after 


40  Principles    of    Optics 

refraction,  but  the  divergence  will  be  less  than  it  was  before 
refraction  (Fig.  15). 

(5)  Rays  which  are  convergent  before  refraction  will  have 
their  convergence  increased  by  the  refraction  (Fig.  16). 

Dispersive  Refraction. — When  rays  proceed  from  a  point 
farther  than  the  center  of  a  concave  surface  separating  two  media, 
the  second  medium  being  the  denser,  the  divergence  of  the  rays 
is  increased,  as  is  shown  in  the  accompanying  diagram  (Fig.  17). 
The  same  effect  results  when  the  rays  pass  from  a  denser  to  a 
rarer  medium  at  a  convex  surface.     Such  refraction,  being  op- 


RARE 


FIG.    17 

posite  in  effect  to  collective  refraction,  is  called  dispersive  refrac- 
tion. It  will  be  more  fully  explained  in  the  consideration  of 
concave  lenses. 

Aberration. — Although  much  larger  pencils  of  light  can 
be  utilized  in  the  production  of  images  by  refraction  than  with  a 
simple  pinhole  opening,  there  is,  nevertheless,  a  limit  to  the  size 
of  the  opening,  which  may  be  used  in  refraction  without  blurring 
of  the  image.  The  opening  must  in  general  be  small  as  compared 
to  the  radius  of  curvature  of  the  separating  surface  and  as  com- 
pared to  the  distance  of  the  point  of  origin  of  the  rays,  for  the 
more  peripheral  rays  are  refracted  too  much  in  proportion  to  the 
medial  rays  of  the  pencil.  This  excess  of  refraction  of  the 
peripheral  rays  gives  rise  to  spherical  aberration. 

The  curvature  of  the  cornea  of  the  normal  eye  is  greatest 
near  its  center  and  diminishes  towards  its  periphery.  In  refrac- 
tion by  a  surface  of  this  form  less  aberration  is  produced  than 
with  a  spherical  surface. 

In  some  cases  of  conical  cornea  the  curvature  is  very  great 
at  the  apex  with  a  rapid  diminution  of  curvature  towards  the 
periphery.     In  such  curvature  the  great  excess  of  central  refrac- 


Refraction    and    Reflection  41 

tion  causes  an  aberration  which  is  opposite  to  that  effected  by 
spherical  surfaces.  This  kind  of  aberration  is  said  to  be  negative, 
in  contradistinction  to  positive  or  spherical  aberration. 

There  is  still  another  kind  of  aberration,  which  is  due  to  the 
fact,  already  mentioned,  that  the  various  colors  do  not  undergo 
the  same  degree  of  deviation.    This  is  called  chromatic  aberration. 

It  can  be  shown  that  aberration  occurs  in  refraction  by  the 
eye,  but  not  ordinarily  to  a  sufficient  extent  to  interfere  with 
vision.  It  is  chiefly  in  the  construction  of  microscopes  and  other 
delicate  optical  instruments  that  aberration  is  a  serious  handicap, 
for  the  neutralization  of  which  much  ingenuity  has  to  be  exer- 
cised. By  the  proper  combination  of  lenses  and  by  the  use  of 
different  kinds  of  glass  (which  we  owe  chiefly  to  the  researches 
of  Abbe)  a  very  high  degree  of  efficiency  can  be  attained. 

Algebraic  Relation  between  Conjugate  Foci. — If  we 
wish  to  determine  the  position  of  the  focus  conjugate  to  a  speci- 
fied point  we  must  make  use  of  the  algebraic  equation  which 
governs  the  relation  between  the  two  foci.  I  shall  show  in  the 
appendix  the  method  by  which  this  formula  is  derived  and  the 
different  forms  in  which  it  may  be  written.  It  suffices  for  our 
present  study  to  give  a  brief  explanation  of  the  symbols  used  in 
the  formula  in  its  simplest  forms. 

It  is  customary  to  denote  the  two  principal  foci  by  the  letters 
F  and  F',  F  being  the  anterior  and  F'  the  posterior  focus,  as 
represented  in  Fig.  12.  It  is  also  customary  to  denote  in  the 
algebraic  formula  the  distances  of  these  two  foci  from  the  surface 
(at  its  intersection  with  the  optic  axis)  by  the  same  symbols; 
that  is,  F  denotes  the  anterior  focal  distance  and  F'  the  posterior 
focal  distance.  The  two  conjugate  focal  distances,  A  0  and  A  I 
are  denoted  by  /  and  /'  respectively;  the  radius  of  the  surface 
is  expressed  by  r,  and  the  indices  of  the  two  media,  by  n  and  nx 
respectively.  If  the  surface  is  convex  r  is  positive  (+),  and  if 
it  is  concave  r  is  negative  ( — ). 
The  anterior  focal  distance  is  derived  from  the  equation 

n   r 

(a). 


«,  —  n 


The  posterior  focal  distance  is  derived  from  the  equation 


S^-T-    (b). 

n,   —  n 


42  Principles    of    Optics 

By  the  proper  substitution  of  these  values  it  is  found  that  the 
equation  which  expresses  the  relation  between  conjugate  points 
may  be  written  in  the  form 

F  Ff 

f  +  jy  =  x  (c)- 

If  we  denote  the  distance  of  the  anterior  principal   focus 

from  the  anterior  conjugate,  0  F,  by  /,  and  the  corresponding 

distance,  I F'  { from  the  posterior  principal  focus  to  the  posterior 

conjugate),   by   /',   the    foregoing   equation   can   be   reduced   to 

the  form 

/  //  =  F  F>    (d). 

This  equation  is  the  more  convenient  when  we  wish  to  de- 
termine the  distance  of  the  conjugate  focus  from  the  principal 
focus,  while  the  first  is  better  when  we  wish  to  ascertain  the 
position  of  the  conjugate  with  reference  to  the  refracting  surface. 

Formation  of  Images  by  Refraction. — The  manner  in 
which  an  object  is  reproduced  in  an  image  is  illustrated  in  Fig.  18, 
in  which  A  is  the  refracting  surface,  C  the  center  of  curvature, 
and  the  focus  /  is  conjugate  to  0.  It  is  apparent  that  Ix  is  con- 
jugate to  Oj,  and  h  to  02.  The  rays  emanating  from  O  are 
therefore   focused  at  /;  those   from   02  at  Ils  and  those   from 


o  *=aX: 


FIG.    l8 

02  at  /„.  In  the  same  way  every  other  point  of  the  object 
Ox  02  has  its  corresponding  focus  on  the  line  Ix  I2,  and  this 
line  is  therefore  an  image  or  reproduction  of  Ox  02.  We  see 
that  Oj  02  and  Iy  I2  are  arcs  of  circles  whose  radii  are  O  C 
and  /  C  respectively ;  but  since  these  arcs  are  very  small  in  com- 
parison with  the  radii,  they  differ  inappreciably  from  straight 
lines.  We  may  therefore,  without  any  material  error,  say  that 
the  image  of  a  straight  line  Ox  02  perpendicular  to  the  axis  O  I 
at  O  is  a  straight  line  Ix  I2  perpendicular  to  the  axis  at  / ; 
or,   since  this  is   true   in   all   meridians,   we   say  that   an   object 


Refraction    and    Reflection 


43 


situated  in  a  plane  perpendicular  to  the  axis  0  I  has  its  image  in 
a  conjugate  plane  also  perpendicular  to  this  axis. 

The  axis  0  I  is  called  the  primary  axis.  All  other  axes,  as 
01  /x  and  02  I2  are  called  secondary  axes. 

Relative  Size  of  Object  and  Image. — It  is  apparent 
from    the    diagram    (Fig.    19)    that    the    relative    size    of   the 


fig.  19 

object  and  its  image  is  determined  by  the  ratio  of  the  distances 
0  C  and  /  C.     This  is  expressed  in  an  equation  as  follows : 

i  (image)  /    C 

o  (object)  O  C 

Cardinal  Points  and  Planes. — The  cardinal  points  of  a 
single  refracting  surface  are  the  two  principal  foci,  the  center 
of  curvature,  and  the  point  where  the  surface  and  primary  axis 
intersect.  The  center  of  curvature  is  called  the  optic  center  or 
the  nodal  point,  and  the  point  of  intersection  of  the  surface  and 
the  axis  is  called  the  principal  point.  The  cardinal  planes  are 
imaginary  planes  meeting  the  axis  perpendicularly  at  the  two 
principal  foci  and  at  the  principal  point. 

By  means  of  the  cardinal  points  we  can  make  a  diagrammatic 
construction  of  the  incident  and  refracted  rays,  and  we  can  deter- 
mine therefrom  the  position  and  size  of  the  image.  The  way 
in  which  we  do  this  is  shown  in  Fig.  19,  in  which  0  C\  represents 
the  linear  dimension  (or  one-half  of  this  dimension  if  the  center 
of  the  object  lies  on  the  optic  axis),  F  and  F'  represent  the  two 
principal  foci,  and  H  H1  the  principal  plane. 

'  Draw  0X  Hlf  representing  a  ray  parallel  to  the  axis  O  I; 
since  all  rays  which  are  parallel  to  the  axis  before  refraction 
must  pass  through  the  posterior  principal  focus  after  refraction, 
Ht  Ilt  passing  through  F' ,  represents  the  course  of  the  refracted 
ray.  Next  draw  0X  H,  representing  a  ray  passing  through  F, 
the  anterior  principal  focus ;  such  a  ray  must  be  parallel  to  the 
axis  after  refraction ;  it  will  be  represented  by  H  Ilm     The  point 


44  Principles    of    Optics 

It  where  the  refracted  rays  intersect  must  be  conjugate  to  Ov 
and  /  Ilt  will  represent  the  image  of  O  0t. 

It  will  be  noticed  that  the  rays  have  been  drawn  as  if  re- 
fracted, not  at  the  curved  surface,  but  at  the  principal  plane. 
The  error  thus  incurred  is  too  slight  to  be  of  practical 
importance,  since  the  focal  distances  are  very  great  in  com- 
parison with  the  distance  between  the  curved  surface  and  the 
tangent  plane. 

The  size  of  the  image  is  determined  by  the  ratio  of  O  C 
to  /  C,  the  relative  distance  of  object  and  image  from  the  nodal 
point,  as  we  have  already  learned;  or  it  may  be  determined  by 
the  ratio  of  A  F  (the  anterior  focal  distance)  to  O  F  (the 
distance  of  the  object  from  this  focus),  since  A  H  is  equal  to 
I  Iv  and  the  triangles  AF  H  and  O  F  01  are  similar. 

The  relation  of  the  object  to  the  image,  as  regards  their 
respective  linear  dimensions,  may  be  expressed  by  the  following 
double  equation: 

i  (image)  A  F  I  C 

o  (object)       :    O   F  ~~  ''    O  C 

It  is  apparent  from  the  foregoing  diagrams  that  real  images 
are  inverted  relatively  to  the  objects  from  which  they  are  formed. 
Virtual  images  are  not  inverted. 

Spherical  Lenses 

A  lens  is  defined  as  a  portion  of  refracting  material  bounded 
by  one  plane  and  one  curved  surface  or  by  two  curved  surfaces. 
Lenses  are  divided  into  two  general  classes,  symmetrical  and 
asymmetrical.  In  symmetrical  lenses  the  curvature  is  spherical, 
and  it  is  with  lenses  of  this  kind  that  we  are  now  concerned. 


fig.  20 


The  various  forms  in  which  lenses  are  made  are  shown 
in  the  accompanying  illustration  (Fig.  20).  They  are  classified 
as  (1)  bi-convex,  (2)  plano-convex,  (3)  concavo-convex,  (4) 
bi-concave,    (5)   plano-concave  and    (6)   convexo-concave.     The 


Refraction    and    Reflection  45 

lenses  comprised  in  the  first  group  of  three  are  all  convex,  for 
the  concavity  of  the  third  lens  of  this  group  is  less  than  the  con- 
vexity of  the  other  surface.  The  lenses  in  the  second  group  of 
three  are  all  concave. 

A  concavo-convex,  or  convexo-concave  lens  is  called  a 
meniscus  {moon-shaped  or  crescent),  or  in  ophthalmology-,  a 
periscopic  lens,  because  when  the  concave  side  is  placed  towards 
the  eye  it  affords  a  more  extensive  field  of  view  than  a  plano- 
convex or  double  convex  lens. 

The  refractive  action  of  a  lens  depends,  of  course,  upon  its 
density  or  refractive  index  with  reference  to  the  medium  by 
which  it  is  surrounded.  In  our  study  of  lenses  it  is  to  be  under- 
stood that  the  refractive  index  of  the  lens  is  greater  than  that 
of  the  surrounding  medium.  The  surrounding  medium  is  air 
in  all  the  lenses  which  we  consider,  with  the  exception  of  the 
crystalline  lens  of  the  eye. 

•  The  straight  line  which  passes  through  the  centers  of  the 
surfaces,  or  which  is  perpendicular  to  both  surfaces,  is  the 
(primary)  axis  of  the  lens. 

The  thickness  of  a  lens  is  the  distance  between  the  two 
surfaces  as  measured  on  the  axis. 

In  the  lenses  which  are  used  in  the  practice  of  ophthalmology, 
however,  we  take  no  regard  of  the  thickness,  for  this  is  so 
slight  as  compared  with  the  focal  length  that  its  consideration 
is  of  no  moment. 

Convex  Lenses. — All  convex  lenses  are  collective  or  con- 
vergent in  action.  In  the  case  of  the  biconvex  lens  the  rays 
which  diverge  from  a  point  are  affected  collectively  first  at 
the  convex  surface  of  incidence  and  then  traversing  the  dense 
material  of  the  lens  they  are  again  refracted  collectively  in  passing 
from  this  dense  material  into  the  air  at  the  second  surface,  which 
is  concave  to  incident  rays.  Of  the  total  effect  produced  by  the 
convex  lens  the  part  which  each  surface  takes  depends  upon 
the  relative  curvature  of  the  two  surfaces  and  upon  the  position 
of  the  point  of  origin  of  the  rays.  In  the  plano-convex  lens, 
for  instance,  rays  diverging  from  a  near-point  will  be  refracted 
collectively  at  both  surfaces,  but  if  the  incident  rays  are  parallel 
the  total  effect  of  the  lens  is  produced  at  the  second  surface. 
In  the  periscopic  convex  lens  the  effect  of  the  refraction  at 
the  concave  surface  will,  in  general,  be  divergent,  but  this  will 


46 


Principles    of    Optics 


be  more  than  neutralized  by  the  refraction  at  the  convex  surface. 

What  we  learned  as  to  the  relative  position  of  conjugate 
foci  in  refraction  at  a  single  spherical  surface  applies  in  the 
main  to  refraction  by  convex  lenses,  as  follows: 

(i)  The  two  principal  foci  are  real  and  the  two  principal 
focal  distances  are  equal  (Fig.  21).  In  the  latter  respect  lens 
refraction  differs  from  refraction  at  a  single  surface. 

(2)  Rays  proceeding  from  a  point  on  the  axis  will  be  brought 


fig.  21 


to  a  real  focus  on  the  opposite  side  of  the  lens,  as  long  as  the 
point  of  origin  is  farther  from  the  lens  than  the  principal  focus 
(Fig.  22). 

(3)   Rays  which  are  parallel  to  the  axis  before  refraction 
will  be  brought  to  a  focus  at  the  posterior  principal  focus,  and 


fig.  22 


rays  proceeding  from  the  anterior  principal  focus  will  be  parallel 
after  passing  through  the  lens  (Fig.  21). 

(4)  Rays  proceeding  from  a  point  on  the  axis  nearer  than 
the  principal  focus  will  remain  divergent  after  passing  through 


U-~-rr-  0. 


FIG.  23 


the  lens  and  will  appear  to  proceed  from  a  virtual  focus  (Fig.  23). 
(5)  Rays  which  are  convergent  before  refraction  will  have 
their  convergence  increased  in  passing  through  the  lens  (Fig.  23 
— by  reversing  the  course  of  the  rays). 


Refraction    and    Reflection 


47 


Formation  of  Images  by  Convex  Lenses. — A  real,  in- 
verted image  will  be  formed  by  a  convex  lens  when  the  object 
is  farther  from  the  lens  than  the  principal  focus  (Fig.  24). 


FIG.    24 


When  the  object  is  at  one  principal  focus  no  image  will  be 
formed,  for  the  rays  from  any  point  of  the  object  will  be 
parallel  after  refraction  (Fig.  25). 

When   the   object   is   so   far   distant  that   the   rays   may  be 


FIG.    25 


regarded  as  parallel,  the  image  will  be  formed  at  the  posterior 
principal  focus. 

When  the  object  is  nearer  than  the  principal  focus,  the  image 
will  be  on  the  same  side  of  the  lens  as  the  object  and  it  will 
be  virtual. 

We  see  that  in  the  diagrammatic  construction  of  the  real 
image  (Fig.  24)  the  ray  01I1  is  represented  as  passing  through 
the  lens  without  deviation.  In  this  respect  it  corresponds  to  the 
nodal  ray  passing  through  the  center  of  a  single  refracting  sur- 
face. The  center  of  a  (thin)  lens  is  in  fact  its  nodal  point,  and  the 
oblique  rays  which  pass  through  this  point  are  secondary  axes, 
since  they  undergo  no  deviation.  The  reason  of  this  is  that  for  all 
such  rays  the  lens  acts  like  a  plate  with  parallel  faces ;  the  devia- 
tion at  one  surface  is  neutralized  by  that  at  the  other  (Fig.  26). 
In  thick  lenses  the  nodal  rays  undergo  lateral  displacement,  but 


48 


Principles    of    Optics 


any  such  displacement  can  be  neglected  in  thin  lenses.  The 
method  of  construction  of  the  image  is  therefore  similar  to  that 
which  we  have  learned  to  apply  in  refraction  at  a  single  surface. 
Concave  Lenses. — In  refraction  by  a  biconcave  lens  rays 
which  diverge  from  a  point  beyond  the  center  of  curvature  of 
the  first  surface  have  their  divergence  increased  at  each  face  of 


fig.  26 

the  lens ;  while  rays  which  diverge  from  a  point  within  the  center 
of  curvature  have  their  divergence  diminished  at  the  first  surface, 
but  this  diminution  is  more  than  overbalanced  by  the  increase  of 
divergence  which  occurs  at  the  second  surface ;  so  also  in  a  plano- 
concave or  a  convexo-concave  lens  the  increase  of  divergence 
which  takes  place  at  the  concave  surface  more  than  neutralizes 


fig.  27 


the  diminution  of  divergence  which  takes  place  at  the  other  sur- 
face. All  concave  lenses  are  therefore  divergent  or  dispersive 
in  action. 

(1)  We  thus  see  that  rays  which  diverge  from  a  point  will 
never  be  united  in  a  real  focus  by  a  concave  lens ;  they  will 
appear  to  diverge  from  a  point  nearer  the  lens  than  the  point 
of  origin  (Fig.  27). 

(2)  Rays  which  are  parallel  to  the  axis  before  entering  the 
lens  will  be  rendered  divergent,  so  that  they  will  appear  to  have 
passed  through  the  principal  focus  (F'  Fig.  28). 

(3)  Rays  which  are  converging  to  the  principal  focus   (F, 


Refraction    and    Reflection 


49 


Fig.  28)  before  entering  the  lens  will  be  rendered  parallel  to  the 
axis  after  passing  through  the  lens. 

Cardinal  Points  of  Lenses. — The  cardinal  points  of  a  thin 
lens  are  the  tzvo  principal  foci  and  the  nodal  point.  By  means  of 
these  points  the  image  may  be  constructed  (Fig.  24). 

Algebraic  Relation  between  Conjugate  Foci  in  Lens 
Refraction. — The  equation  which  expresses  the  relation  be- 
tween conjugate  points  in  lens  refraction  is  determined  by  apply- 
ing the  equation  for  refraction  at  a  single  spherical  surface  to 
the  first  and  then  to  the  second   refraction.     It   is  thus   found 


fig.  28 


that  in  a  lens  the  two  principal   focal  distances  are  equal  and 
that  the  algebraic  equation  between  conjugate  points  becomes 


f 


+ 


=  1,  or  1 1' 


F'' 


The   method   of   derivation   of   these   equations   is   given   in  the 
appendix. 

Numeration  of  Lenses. — Lenses  may  be  numbered  in 
accordance  with  their  focal  length  or  with  their  refractive 
power,  the  latter  being  inversely  proportional  to  the  former.     If 

F  expresses  the  focal  length  of  a  lens  -L  expresses  its  refractive 

power. 

Ophthalmic  lenses  are  usually  made  of  glass  of  which  the 
index  is  about  1.52.  Upon  the  assumption  that  this  index  is 
(approximately)  1.5  we  can  readily  prove  from  the  proper 
algebraic  equation  that  the  focal  length  is  twice  the  radius  of 
curvature  (21')  if  the  lens  is  piano-curved,  and  that  it  is  equal 
to  the  radius  (r)  if  each  face  of  the  lens  is  equally  curved.  With 
this  understanding  therefore  the  equal  curvature  (  l  )  ground  on 
each  face  of  the  lens  may  be  taken  as  the  measure  of  the  lens. 


50  Principles    of    Optics 

In  this  system,  which  is  the  old  method  of  numbering  lenses,  the 
inch  is  the  unit  of  measurement  and  the  unit  lens  is  a  lens  whose 
focal  length  is  presumably  one  inch,  because  the  radius  of 
curvature  of  each  face  is  one  inch. 

This  system  is  possessed  of  a  number  of  disadvantages.  In 
the  first  place,  the  inch  is  not  a  fixed  unit ;  it  varies  in  different 
countries.  Secondly,  owing  to  the  fact  that  the  refractive  index 
is  greater  than  1.5,  the  focal  length  is  in  reality  less  than 
is  indicated  by  the  radius  of  curvature,  in  accordance  with  which 
the  lenses  are  numbered. 

These  two  disadvantages  of  the  inch  system  are  perhaps  of 
minor  importance,  but  there  is  a  third  disadvantage  which  is  of 
a  more  serious  nature.  This  is  that,  owing  to  the  comparatively 
great  refractive  power  of  the  unit  lens,  this  power  must  be 
expressed  as  a  fraction  in  all  those  lenses  which  are  commonly 
used  in  ophthalmology.  Thus  a  lens  whose  focal  length  is 
twenty  inches  has  a  power  JU  as  great  as  the  unit  lens.  The 
power  of  a  40-inch  lens  is  expressed  by  -^- ,  and  so  on.  These 
fractional  expressions  are  very  inconvenient  in  the  addition  or 
subtraction  of  lenses,  since  the  combined  action  of  two  thin 
lenses  is  equal  to  the  sum  of  the  powers  of  the  lenses. 

The  disadvantages  of  the  foregoing  method  are  overcome 
in  the  metric  system  of  numbering  lenses.  This  system  was 
introduced  by  Nagel  in  1866.  In  it  the  unit  is  the  meter  lens, 
or  lens  whose  focal  length  is  one  meter.  The  power  of  this 
lens  is  now  universally  expressed  by  the  word  diopter,  or  dioptry, 
which  was  brought  into  use  by  Monoyer. 

The  diopter  (1  D)  expresses  the  power  of  a  lens  whose  focal 
length  is  one  meter.  A  lens  whose  focal  length  is  one-half  of  a 
meter  is  expressed  by  2  D,  while  a  lens  whose  focal  length  is 
two  meters  is  expressed  by  0.50  D,  and  so  on. 

Although  this  method  has  entirely  replaced  the  inch  system 
in  ophthalmology  it  is  important  that  one  should  know  how  to 
transform  the  lens  number  from  one  system  to  the  other.  This 
transformation  is  easily  made  if  we  remember  that  the  meter  is 
approximately  equal  to  40  English  inches  and  that  the  focal 
length  as  expressed  in  inches  will  be  40  times  as  many  units 
as  when  expressed  in  terms  of  the  meter.  A  lens  whose  focal 
length  is  one  meter  will  be  measured  by  the  number  40  (a  40- 
inch  lens)  in  the  inch  system;  the  focal  length  of  a  lens  of  3  D 


Refraction    and    Reflection  51 

will  be  expressed  by  ^  in  inches,  or  it  will  be  approximately 
represented  by  a  13-inch  lens.  Conversely,  the  dioptric  number 
is  obtained  by  dividing  40  by  the  lens  number  as  expressed  in 
inches.  We  may  express  the  relation  between  the  two  systems 
in  the  following  equation: 

Dioptric  number  X  inch  number  =  40.* 

Reflection  at  Spherical  Surfaces 

Reflection   at   a  convex   spherical   surface   is   illustrated  in 
Fig.  29,  in  which  5  £  represents  the  reflecting  surface  and  0  Ot 


fig.  29 

the  object  whence  the  rays  of  light  proceed.  From  the  point  0 
rays  diverge,  some  of  which  meet  the  convex  surface  and  are 
reflected  from  it  in  accordance  with  the  law  of  reflection  that 
the  angles  of  incidence  and  reflection  are  equal.  Some  of  these 
rays  may  enter  an  eye  or  a  telescope  situated  at  E.  The  various 
reflected  rays  if  prolonged  backward  would  meet  at  the  virtual 
focus  /.  In  the  same  way  the  rays  proceeding  from  Ox  would 
meet  at  I13  and  /  Ix  is  the  virtual  image  of  O  Ox. 

The  rays  O  C  and  Ox  C,  which  are  directed  towards  the  center 
of  the  surface  are  the  nodal  rays  and  the  size  of  the  image  is 
determined,  as  in  refraction,  by  the  respective  distances  of  object 
and  image  from  the  nodal  point.    Thus, 

i  (imape)  I  C 

o  (object)  O  C  ' 

When  the  object  is  so  far  distant  that  the  rays  may  be  re- 
garded as  parallel,  the  image  is  formed  at  the  principal  focus  of 
the  mirror.f  This  principal  focus  lies,  as  the  algebraic  equation 
shows,  half  way  between   the   surface   and   its   center.     As   the 


*If  the  Paris  inch  is  used  the  number  40  should  be  replaced  by  36. 
t'l'he  two  principal  foci  coincide  iu  position  in  reflection. 


52  Principles    of    Optics 

object  approaches  the  mirror  the  image  behind  the  mirror  also 
approaches  the  surface.  The  image  is  always  virtual,  erect  and 
smaller  than  the  object. 

Images  of  this  kind  are  formed  by  reflection  at  the  surfaces 
of  the  cornea  and  at  the  anterior  surface  of  the  crystalline  lens, 
and  it  is  by  means  of  these  images  that  we  determine  the  radii  of 
curvature  of  the  surfaces. 


fig.  30 

Reflection  at  a  concave  surface  is  illustrated  in  Fig.  30,  in 
which  5"  6"  represents  the  concave  surface  and  O  0X  the  object 
whence  the  rays  proceed.  In  this  case  a  real  inverted  image 
of  the  object  is  formed  at  /  It.  The  size  of  this  image  is 
governed  by  the  same  formula  as  that  given  above  for  convex 
mirrors.  As  in  the  convex  mirror,  the  principal  focus  lies  half 
way  between  the  surface  and  its  center.  A  real  inverted  image 
of  this  kind  is  formed  by  reflection  at  the  posterior  surface  of 
the  crystalline  lens,  and  by  the  measurement  of  this  image  we 
determine  the  radius  of  curvature  of  the  surface. 

Spherical  aberration  occurs  in  images  by  reflection  as  it 
does  in  refraction,  but  not  to  an  extent  great  enough  to  materially 
affect  the  result  in  such  measurements  as  we  have  to  make. 

In  the  convex  mirror  the  principal  focus  is  behind  the  mirror 
and  it  is  impossible  to  place  an  object  at  this  focus,  but  in  the 
concave  mirror  an  object  may  be  so  placed  and  the  rays  reflected 
by  the  mirror  under  this  condition  will  be  parallel. 

If  we  place  an  object  at  /  Ir  the  image  will  be  represented 
by  0  0lt  for  the  two  conjugate  foci  are  interchangeable. 

When  the  object  is  nearer  the  mirror  than  the  principal  focus 
the  image  will  be  virtual,  erect  and  larger  than  the  object. 

Thus  we  see  that  convex  mirrors  have  a  divergent  effect 
and  concave  mirrors  a  convergent  effect  upon  light  rays,  which, 
as  we  know,  is  opposite  to  the  action  of  these  surfaces  in  re- 
fraction. 


Refraction    and    Reflection  53 

Algebraic  Relation  between  Conjugate  Foci  in  Reflec- 
tion.— The  different  conditions  of  reflection  may  be  verified 
and  the  position  of  conjugate  foci  determined  by  the  algebraic 
equation  which  expresses  the  relation  between  these  foci. 

Any  formula  for  refraction  may  be  converted  into  the  cor- 
responding formula  for  reflection  by  imposing  the  condition  that 
the  refractive  index  is  equal  to  minus  one  (n  =  —  1).  This 
comes  by  making  the  angles  i  (incidence)  and  r  (reflection)  equal 
but  of  opposite  signs. 

By  making  this  change  in  (a)  and  (b),  p.  41,  we  derive  the 
position  of  the  principal  focus  of  a  spherical  mirror  from  the 
equation 

F*=  —  =  —  Fr. 

2 

The  following  authorities  have  been  consulted  in  the  prep- 
aration of  the  foregoing  chapter  : 

Gage,  Elements  of  Physics. 

Ganot,  Physics. 

Heath,  Geometrical  Optics. 

Juler,  Ophthalmic  Science  and  Practice. 

Preston,  Theory  of  Light. 

Abbe,  Ueber  Verbesserung  des  Mikreskops  mit  Hilfe  neuer 
Art  en  Opt.  Glasses. 

Nagel,  Die  Anomalieen  der  Ref.  und  Accom.  des  Auges, 
Graefe-Saemisch  Handbuch,  1st  ed. 

Landolt,  Introduction  of  the  Metrical  System  into  Ophthal- 
mology, Royal  London  Ophthal.  Hosp.  Reports,  vol.  viii,  part  iii. 

Burnett,  The  Meter-Lens,  Its  English  Name  and  Equivalent, 
N.  Y.  Med.  Jour.,  1886. 


CHAPTER  IV 


COMPOUND  OPTICAL  SYSTEMS 

A  series  of  spherical  surfaces  bounding  media  of  different 
density,  all  the  surfaces  being  centered  on  a  common  axis,  con- 
stitutes a  compound  optical  system.  Refraction  by  a  compound 
system  is  illustrated  in  Fig.  31.  The  point  from  which  the 
rays  diverge  is  represented  by  O.  The  rays  diverging  from  this 
point  are  refracted  at  the  first  surface  Ar  so  that  they  are 
directed  towards  It,  but  before  reaching  Ix  they  undergo  a  second 


FIG.   31 


refraction  at  the  surface  A2.  This  refraction  in  our  illustration 
is  divergent  and  the  rays  are  now  directed  towards  I2,  but  before 
reaching  this  point  they  are  again  refracted  at  A3>  and  finally 
after  the  fourth  refraction  at  the  surface  A±  they  are  united 
in  a  focus  at  74. 

It  was  first  demonstrated  by  Gauss,  an  eminent  mathema- 
tician of  the  eighteenth  century,  that  two  points  which  are  con- 
jugate in  the  refraction  by  a  compound  system  of  any  number  of 
surfaces  are  related  by  the  same  algebraic  formula  as  in  a  single 
refraction.  There  is  this  difference,  however,  that  the  foci 
are  not  measured  from  a  single  point  (the  principal  point),  but 
from  two  principal  points  separated  by  an  interval.  The  anterior 
focal  distances  are  measured  from  the  first  principal  point,  while 
the  posterior  focal  distances  are  measured  from  the  second  princi- 
pal point. 

(54) 


Compound    Optical    Systems 


55 


The  principal  points  are  defined  as  two  points  which  are  con- 
jugate in  the  refraction  by  the  entire  system,  and  which  are  so 
situated  that  a  ray  directed  towards  a  point  in  one  principal 
plane  will  appear  after  refraction  to  proceed  from  a  point  in  the 
other  principal  plane,  the  two  points  lying  on  the  same  side  of 
the  axis  and  equidistant  from  it.  The  principal  points  are  repre- 
sented by  H  and  H',  and  the  principal  planes  by  E  H  and  E'  H' . 

Cardinal  Points  of  a  Compound  System. — The  cardinal 


FIG.   32 

points  of  a  compound  system  are  the  two  principal  foci,  the  two 
principal  points  and  the  two  nodal  points.  The  interval  between 
the  two  nodal  points  is  the  same  as  that  between  the  two  princi- 
pal points.  The  cardinal  points  and  their  planes  and  the  diagram- 
matic construction  of  the  image  are  shown  in  Fig.  32. 

The  Eye 

The  eye  constitutes  a  compound  system  of  four  surfaces,  such 
as  is  illustrated  in  Fig.  31. 

Of  the  four  surfaces  which  constitute  this  system  the  first 
and  the  most  effective  is  the  anterior  surface  of  the  cornea.  This 
surface  is  convex  to  incident  light  and  the  index  of  the  corneal 
tissue  is  greater  than  that  of  the  air  from  which  the  light  comes. 
The   refraction  which   occurs   at  this   surface   is   therefore   con- 

: 

vergent. 

The  posterior  surface  of  the  cornea,  at  which  light  passes 
into  the  aqueous  humor,  is  the  second  surface  of  this  system. 
This  surface  is  also  convex.  In  this  case,  however,  the  light 
is  passing  from  a  denser  to  a  rarer  medium,  for  the  index  of 
the  aqueous  humor  is  less  than  that  of  the  cornea.  The  effect 
of  this  refraction  is,  therefore,  a  partial  neutralization  of  the 
convergent  action  of  the  anterior  surface. 

The  anterior  surface  of  the  crystalline  lens  is  the  third  sur- 
face of  the  system.  This  surface  is  convex  to  the  incident  rays 
and  the  index  of  the  lens  is  greater  than  that  of  the  aqueous 
humor,  and  therefore  this  refraction  is  convergent. 


56 


Principles   of    Optics 


The  fourth  and  last  surface  is  the  posterior  surface  of  the 
crystalline  lens,  where  the  rays  enter  the  vitreous  body.  This 
surface  is  concave  to  incident  rays  which  are  passing  from  a 
denser  to  a  rarer  medium.    The  refraction  is  therefore  convergent. 

The  crystalline  lens  is  not  a  homogeneous  substance.  Its  re- 
fractive index  gradually  increases  from  the  cortex  to  the  nucleus. 
We  must,  therefore,  for  the  purpose  of  calculation,  substitute 
for  the  natural  lens  an  ideal  body,  which  has  the  same  refractive 
effect  as  the  crystalline  lens.  Helmholtz  and  others  have,  by 
very  exact  measurements,  determined  the  refractive  power  of  the 


fig.  33 

Illustrating  the  relative  action  of  the  cortical  and  nuclear  portions  of  the  crystalline 

lens  (Landolt). 

human  lens,  thereby  making  it  possible  for  us  to  substitute  for 
this  lens  an  equivalent  lens  which  has  the  same  curvatures  and 
thickness  as  the  natural  lens,  but  a  uniform  index. 

The  equivalent  index  of  the  crystalline  lens  is  not,  as  one 
might  suppose,  the  average  of  the  indices  of  the  component  por- 
tions of  the  lens.  It  is,  on  the  contrary,  higher  than  the  highest 
index  of  the  natural  lens.  This  is  because  the  curvature  of  the 
nucleus  is  greater  than  that  of  the  cortex,  so  that  this  cortex 
acts  as  two  divergent  menisci  would  act  if  applied  to  the  nucleus 
in  such  manner  as  to  neutralize  a  part  of  the  convergent  action 
of  the  nucleus  (Fig.  33).  If  the  index  of  these  two  menisci 
were  as  high  as  that  of  the  nucleus,  they  would  neutralize  more 
of  the  convergent  action  of  the  highly  curved  nucleus  than  they 


Compound    Optical    Systems  57 

do  as  they  are  constituted  with  a  lower  index,  so  that  if  the 
whole  lens  had  the  index  of  the  nuclear  portion,  its  convergent 
action  would  be  less  than  it  actually  is.  It  is  therefore  apparent 
that  an  effect  equal  to  that  of  the  crystalline  lens  may  be  obtained 
by  means  of  an  ideal  lens  of  corresponding  curvature  and  of 
uniform  index  only  if  this  index  is  higher  than  the  index  of  the 
nuclear  portion  of  the  natural  lens. 

As  we  are  able  to  simplify  the  study  of  the  refractive  action 
of  the  eye  by  substituting  the  equivalent  for  the  natural  lens, 
so  we  may  still  further  simplify  this  study  by  assigning  to  the 
cerneal  tissue  the  lower  index  of  the  aqueous  humor.  The 
thickness  of  the  cornea  is  very  slight  (1  mm)  and  there  is  very 
little  difference  between  the  index  of  the  cornea  and  that  of  the 
aqueous. 

We  may  therefore  disregard  the  cornea  entirely  and  assume 
that  the  rays  enter  the  aqueous  humor  directly  from  the  anterior 
surface  of  the  cornea.  The  optic  system  of  the  eye,  with  this 
assumption,  consists  of  three  surfaces  and  three  media,  and  we 
may  consider  it  as  composed  of  a  single  refracting  surface  (the 
cornea)  in  combination  with  a  single  lens  (the  crystalline). 

Although  for  ordinary  purposes  of  study  we  may  make  this 
assumption,  we  find  that  the  mathematical  eye  deduced  under 
this  condition  is  appreciably  shorter  than  that  which  results  from 
the  consideration  of  all  four  surfaces.  Therefore,  in  order  to 
obtain  a  mathematical  result  agreeing  as  closely  as  possible  with 
the  length  of  the  human  eye  as  determined  from  anatomical  ex- 
amination, I  have  used  all  four  surfaces  in  my  calculations  which 
are  given  in  the  appendix. 

Formation  of  Images  by  the  Eye. — Since  the  eye  consti- 
tutes a  convergent  refractive  apparatus,  it  is  apparent  that  rays 
of  light  entering  an  eye  from  an  external  object  (situated  without 
the  anterior  focus  of  the  eye)  will  be  brought  to  a  real  focus 
at  some  point  behind  the  cornea  and  that  a  real  inverted  image 
of  the  object  will  be  formed,  as  is  represented  in  Fig.  34. 

The  fact  that  the  image  is  inverted  has  led  some  persons  to 
wonder  why  we  do  not  see  objects  in  an  inverted  position.  It  is 
only  necessary  to  bear  in  mind  that  we  do  not  see  the  retinal 
image  at  all.  This  image  does  not  enter  into  the  consciousness 
of  vision. 

By  an  innate  mental   faculty   we   assume   that   stimulation 


58  Principles   of    Optics 

received  through  certain  fibers,  which  in  turn  are  connected  with 
a  certain  part  of  the  retina,  is  produced  by  an  object  situated 
in  a  certain  direction.  Since  light  proceeding  from  points  on 
the  left  must  (under  ordinary  conditions)  stimulate  certain  points 
on  the  right  side  of  the  retina,  and  vice  versa,  we  assign  to 
objects  their  position  in  space  in  accordance  with  this  fact. 

The  relative  direction  of  any  point  in  space  from  its  image 
on  the  retina  can  only  be  expressed  by  the  straight  line  which 
joins  these  two  points.  In  a  single  refraction  the  nodal  ray  is  a 
straight  line  connecting  any  point  of  an  object  with  the  cor- 
responding point  of  its  image,  but  when  in  a  compound  system 
the  nodal  ray  undergoes  lateral  displacement,  this  ray  is  not  a 
straight  line.  In  the  eye  the  lateral  displacement  is  practically 
imperceptible,  since  the  interval  between  the  two  nodal  points  is 
only  .37  mm.  We  may  therefore  regard  the  nodal  ray  as  the 
line  of  visual  projection  (Fig.  34). 


fig.  34 

Relative  Size  of  Object  and  Image. — We  have  the  same 
equations  for  determining  this  relation  as  we  have  in  simple 
systems : 

i    (image)  IN'  HF 

o  (object)  O  N  '      O  F'     ^,g'32J 

Of  these  two  relations  the  former — that  is,  the  ratio  of  the 
distances  of  the  object  and  its  image,  respectively,  from  the  nodal 
point — is  perhaps  the  more  convenient  for  general  use;  but  when 
we  wish  to  compare  the  images  of  the  same  object  as  formed 
by  different  refractive  systems  we  find  it  easier  to  make  use 
of  the  second  relation.  In  making  the  comparison  of  different 
systems  we  see  that  as  long  as  the  distance  (OF)  of  the  object 
from  the  anterior  focus  is  unchanged  the  linear  dimension  of 
the  image  is  proportional  to  the  anterior  focal  length  of  the  re- 
fracting system. 

The  Visual  Angle. — The  angle  which  an  object,  or  its 
image,   subtends   at   the   nodal   point  of   the   eye   is   called   the 


Compound    Optical    Systems  59 

visual  angle.    In  Fig.  35  the  visual  angle  is  represented  by  0  N  O 
or  INI. 


fig.  35 

The  Schematic  Eye. — The  measurements  of  the  average 
normal  eye,  as  determined  by  calculation,  constitute  the 
schematic  eye.  The  average  values  of  the  various  curvatures, 
indices  and  intervals  between  the  surfaces  have  been  determined 
from  measurements  made  by  scientific  investigators.  A  short 
description  of  the  way  in  which  the  results  were  obtained  will  be 
found  in  a  subsequent  chapter  (The  Normal  Eye).  The  values 
upon  which  we  base  our  calculations  are  given  in  the  following 
table. 

RADII   OF   CURVATURE 

Anterior  surface  of  the  cornea 7.8  mm  (r,) 

Posterior  surface  of  the  cornea       6     mm  (r2) 

Anterior  surface  of  the  lens 10     mm  (r3) 

Posterior  surface  of  the  lens 6     mm  (r4) 

INDICES  THICKNESSES 

Cornea 1.377  (n,)  1      mm  (t,) 

Aqueous  humor 1.337  (n2)  2.6  mm  (t3) 

Lens      1.437  (n3)  4     mm  (t3) 

Vitreous  body 1.337  in4) 

By  substituting  these  values  in  the  proper  equations  and 
imposing  the  required  conditions,  I  have  obtained  the  following 
data  for  the  schematic  eye,  which  is  illustrated  in  Fig.  36. 

From  summit  of  cornea  to  first  principal  point     1-77  mm 

From  summit  of  cornea  to  second  principal  point 2.14  mm 

From  summit  of  coruea  to  first  nodal  point 7.09  mm 

From  summit  of  cornea  to  second  nodal   point 7.46  mm 

From  summit  of  cornea  to  anterior  focus     13.99  mm 

From  summit  of  cornea  to  posterior  focus 23.22  mm 

Anterior  focal  distance  (measured  from  first  principal  point)        .    .  15.76  mm 
Posterior  focal  distance  (measured  from  second  principal  point)  .    .  21.07  mm 

The  Reduced  Eye. — Since  the  interval  between  the  two 
nodal  points  of  the  eye  is  only  .37  mm,  we  may,  for  the  purpose 
of  studying  the  eye  as  a  refractive  apparatus,  neglect  this  interval 
without   any   material   error.     With   this   simplification   the   eye 


60  Principles    of    Optics 

is  comparable  to  a  single  surface  separating  two  media  whose 
indices  are  I  (the  index  of  air)  and  1.337  (^ne  index  of  the 
vitreous)  respectively. 

As  far  as  the  size  of  the  image  is  concerned,  there  is  no 
difference  between  the  compound   system    (the   schematic  eye) 


fig.  36 

The  schematic  or  average  normal  eye.    The  anterior  and  posterior  principal  foci   are  repre- 
sented by  F  and  F'  respectively  ;  the  first  and  second  principal  points   by  //and  H' , 

and  the  nodal  points  by  JVaud  N' 

and  its  simple  substitute,  but  as  regards  the  position  of  the  image, 
we  must  remember  that  in  the  compound  system  all  posterior 
focal  distances  are  measured  from  the  second  principal  point, 
•2,7  mm  from  the  first  principal  point,  and  that  this  dimension 
must  be  added  to  any  conjugate  focal  distance  in  order  that  the 
position  of  the  image  may  conform  to  that  in  the  compound 
system. 

Listing's  Reduced  Eye. — Listing,  who  first  reduced  the 
schematic  eye  to  a  simple  equivalent,  placed  the  imaginary  surface 
between  the  two  principal  points  and  allowed  the  two  principal 
foci  of  the  schematic  eye  to  retain  their  positions.  In  this  substi- 
tution the  focal  distances  are  not  strictly  identical  with  those  of 
the  schematic  eye,  although  the  discrepancy  is  too  slight  to  be 
of  practical  importance.  Listing's  reduced  eye  does  not,  however, 
accurately  represent  the  normal  eye.  This  is  chiefly  because  he 
adopted  too  high  a  refractive  index  (1.4545)  for  the  lens,  so  that 
his  schematic  eye,  on  which  the  reduction  is  based,  is  too  short. 

Donders's  Reduced  Eye. — Of  the  several  other  equivalents 
which  have  been  proposed  for  the  schematic  eye,  only  the  reduced 
eye  of  Donders  requires  mention.  In  this  reduction  the  anterior 
focal  distance  is  15  mm,  the  posterior  focal  distance  is  20  mm  and 
the  radius  of  the  imaginary  surface  is  5  mm. 

These  values  are  taken  because  with  them,  as  we  readily  learn 
from  equation  (a)  the  value  of  n  is  1.333,  which  is  the  index 
of  water. 


Compound    Optical    Systems  61 

While  this  system  does  not  very  closely  approximate  the 
schematic  eye,  it  furnishes  very  convenient  data  for  the  construc- 
tion of  an  artificial  eye  for  the  study  of  refraction. 

The  Aphakic  Eye. — When  the  crystalline  lens  is  not  pres- 
ent in  an  eye  the  eye  is  said  to  be  aphakic.  In  this  condition, 
in  which  the  rays  of  light  pass  directly  from  the  aqueous  to  the 
vitreous  without  the  intervention  of  the  lens,  the  focal  distances 
of  the  eye  differ  materially  from  those  of  the  normal  eye. 

Since  the  aqueous  and  vitreous  have  practically  the  same 
index,  the  aphakic  eye  presents  only  two  surfaces — the  anterior 
and  posterior  surfaces  of  the  cornea.  We  have  learned  that  the 
two  corneal  refractions  may  be  replaced  by  a  single  refraction 
at  the  anterior  surface  of  the  cornea,  which,  therefore,  constitutes, 
in  our  calculations,  the  total  refraction  by  the  aphakic  eye. 

Focal  Distances  of  the  Aphakic  Eye. — From  the  equation 


we   find  that   the   anterior   focus   in  the  corneal   refraction   lies 
23.14  mm  in  front  of  the  cornea,  and  from  the  equation 


F'  = 


n  —  1 


we  find  that  the  posterior  focus  lies  30.94  mm  behind  the  an- 
terior surface  of  the  cornea. 

Relative  Position  of  the  Retina  and  Posterior  Principal 
Focus  of  the  Eye. — The  study  of  this  relation  in  detail  will 
occupy  our  attention  in  subsequent  chapters.  It  suffices  to  state 
here  just  what  this  relation  may  be  and  to  define  the  meaning 
of  the  terms  used,  so  that  we  may  be  able  to  understand  the 
various  optical  problems  which  present  themselves. 

When  the  retina  intersects  the  optic  axis  of  the  eye  at  its 
posterior  principal  focus  the  eye  is  adapted  to  receive  a  clear 
impression  of  a  distant  object.  This  condition,  as  it  occurs 
during  complete  relaxation  of  the  ciliary  muscle,  is  called  em- 
metropia.     Any  deviation  from  emmetropia  is  called  ametropia. 

Hyperopia  is  that  form  of  ametropia  in  which  the  retina  lies 
in  front  of  the  principal  focus  during  relaxation  of  the  ciliary 
muscle,  or  it  is  that  condition  in  which  the  eye  is  relatively  too 
short.     In  hyperopia  the  image  of  a  distant  object,  as  formed  on 


62  Principles    of    Optics 

the  retina  during  relaxation  of  the  ciliary  muscle,  will  be  blurred 
and  the  image  of  a  near  object  will  be  even  more  blurred. 

Myopia  is  that  condition  in  which  the  retina  lies  behind  the 
principal  focus  during  relaxation  of  the  ciliary  muscle,  the  eye 
being  relatively  too  long.  In  myopia  the  image  of  a  distant 
object  will  be  blurred,  but  the  image  of  a  near  object  may  be 
clearly  formed  on  the  retina. 

Astigmia  (astigmatism)  is  that  condition  in  which,  owing 
to  asymmetry  of  curvature  of  one  or  more  of  the  refracting 
surfaces,  the  eye  if  emmetropic  in  one  meridian  will  be  either 
hyperopic  or  myopic  in  a  meridian  at  right  angles  to  the  emme- 
tropic meridian ;  or  the  eye  may  be  hyperopic  or  myopic  in  both 
principal  meridians,  but  more  so  in  one  than  in  the  other.  Or, 
again,  it  may  be  hyperopic  in  one  and  myopic  in  the  other 
meridian. 

Accommodation. — In  the  refraction  by  the  eye  the  position 
of  the  image  is  not  appreciably  altered  by  changing  the  position 
of  the  object  as  long  as  this  distance  is  not  less  than  about  six 
meters,  or  twenty  feet.  For  all  objects  which  are  not  nearer  the 
eye  than  this  limit  we  regard  the  rays  as  being  parallel  and  the 
conjugate  image  as  being  formed  at  the  principal  focus.  But 
when  an  object  is  nearer  than  this  its  conjugate  image  falls  per- 
ceptibly behind  the  principal  focus,  and  consequently  behind  the 
retina  if  the  eye  is  emmetropic,  and  more  so  if  the  eye  is  hy- 
peropic. 

In  order  that  a  near  object  may  be  clearly  seen,  the  image 
must  be  brought  forward  so  that  it  will  be  focused  on  the  retina. 
This  is  normally  accomplished  by  an  increase  in  the  convexity 
of  the  crystalline  lens  under  the  influence  of  the  ciliary  muscle. 
This  adaptation  of  the  eye  for  various  distances  is  called  accom- 
modation. 

Since  accommodation  is  effected  by  a  change  in  the  curvature 
of  the  lens,  the  optical  system  of  the  eye  varies,  in  near  vision, 
with  every  variation  in  the  distance  of  the  object.  The  focal 
distances  are  shortened  by  accommodative  action,  so  that  the 
retina  lies  behind  the  principal  focus  as  in  the  myopic  eye. 

Presbyopia. — The  power  of  accommodation  undergoes  a 
gradual  diminution  with  an  increase  of  age,  so  that  eventually 
the  eye  is  unable  to  adjust  itself  for  near  objects.  When  the 
focusing  power  has   suffered  this  physiological   loss  to  such  a 


Compound    Optical   Systems  63 

degree  that,  after  the  correction  of  any  existing  ametropia,  clear 
vision  is  impossible  at  a  distance  of  22  cm  (9  inches)  the  eye 
is  said  to  be  presbyopic  (Bonders). 

The  following  authorities  have  been  consulted  in  the  prep- 
aration of  the  foregoing  chapter : 

Heath,  Geometrical  Optics. 

Landolt,  Refraction  and  Accommodation  of  the  Eye. 
Gauss,  Dioptrische  Untersuchungen. 
Donders,  Anomalies  of  Refraction  and  Accommodation. 
Listing,  Dioptrik  des  Auges,  Wagner's   Handwdrterbuch  der 
Physiologie. 


CHAPTER  V 


REFRACTION  AT  ASYMMETRICAL  SURFACES 

By  an  asymmetrical  surface  we  mean  a  surface  whose  curva- 
ture, being  regular  or  symmetrical  in  any  meridian,  varies 
by  infinitesimal  gradations  with  a  like  variation  of  the 
meridian. 

In  spherical  surfaces,  to  which  we  have  hitherto  devoted 
our  attention,  the  curvature  is  the  same  in  all  meridians,  and 
in  our  study  of  refraction  we  have  represented  this  curvature 
diagrammatically  by  an  arc  of  a  circle,  which  is  the  curvature 
of  any  section  of  a  sphere.  Since  in  any  other  meridian  the 
curvature  is  the  same,  we  know  that  whatever  deductions  we 
reach  as  to  the  refractive  effect  in  this  meridian  will  be  true  for 
all  meridians.  But  this  will  evidently  not  be  so  in  the  refraction 
which  takes  place  at  asymmetrical  surfaces. 

Principal  Meridians. — Fortunately  we  can  by  the  aid  of 
two  meridians,  those  of  greatest  and  of  least  curvature,  the 
two  being  at  right  angles  to  each  other,  trace  the  path  of  all  rays 
(within  the  limitations  of  our  algebraic  formulae)  which  are  re- 
fracted at  an  asymmetrical  surface.  These  two  meridians  are 
called  the  principal  meridians. 

The  Toric  Surface. — We  may  confine  our  study  of 
asymmetrical  surfaces  to  those  in  which  the  basis  of  curvature 
is  a  circle.  In  the  sphere  the  circle  which  is  the  basal  curvature 
is  the  same  in  all  meridians.  But  the  torus  is  generated  from 
two  circles  of  different  curvature,  lying  in  the  principal  meri- 
dians, at  right  angles  to  each  other. 

The  word  torus,  which  is  of  architectural  origin,  signifies  the 
ring-shaped  base  of  a  column.  This  form  of  curvature  is  shown 
in  Fig.  37  and  Fig.  38. 

Refraction  at  a  toric  surface  is  illustrated  in  Fig.  39,  in  which 
H  H  and  V  V  are  the  principal  meridians.    We  assume  that  the 

(64) 


Refraction  at  Asymmetrical  Surfaces 


65 


horizontal  curvature  H  H  is  greater  than  the  vertical  curvature 
V  V.    First,  we  examine  the  rays  that  enter  the  second  medium 


FIG.    38 


Toric  Curvature   {Prentice) 


in  the  meridian  H  11.  These  rays,  proceeding  from  O,  will  be 
united  in  a  focus  at  /.  Next  we  examine  those  rays  which,  pro- 
ceeding from  0,  enter  the  second  medium  in  the  vertical  meri- 
dian V  V.    These  rays  will  be  united  in  a  focus  at  T. 

As  regards  the  refraction  of  rays  which  lie  in  the  two  princi- 
pal meridians,  therefore,  we  have  no  difficulty  in  understanding 
what  takes  place.  But  when  we  come  to  consider  those  rays 
which  do  not  lie  in  these  meridians,  it  is  not  so  easy  to  form  a 
mental  picture  of  their  refracted  course.  A  common  error,  which 
is  to  be  found  in  many  text-books  of  ophthalmology,  consists  in 
supposing  that  as  there  is  a  focus  for  each  of  the  two  principal 
meridians,  so  there  is  likewise  a  focus  for  each  intermediate  or 
oblique  meridian ;  in  other  words,  that  there  is  a  series  of  foci 
extending  between  the  two  foci  of  the  principal  meridians. 


fig.  39 

Refraction   at   an   Asymmetrical    Surface 


From  a  careful  inspection  of  the  diagram  (Fig.  39)  we  see 
that  all  the  rays  are  so  governed  by  the  horizontal  refraction  that 
they  must  pass  through  the  vertical  line  Ir  I2,  erected  at  the  hori- 


66  Principles    of    Optics 

zontal  focus  /,  and  that  they  are  so  governed  by  the  vertical 
refraction  that  they  must  pass  through  the  horizontal  line  7\  T2, 
passing  perpendicularly  through  the  vertical  focus  T.  These  two 
lines  are  called  the  focal  lines. 

When  the  point  O  is  so  far  distant  that  /  and  T  become 
principal  foci  in  the  two  principal  meridians,  Ix  I2  and  Tl  T2  are 
the  principal  focal  lines,  and  I  T  is  the  principal  focal  interval. 
This  interval  is  also  called  Sturm's  interval,  in  honor  of  the 
demonstrator  of  asymmetrical  refraction. 

The  rays  O  S1  and  O  S2  lie  in  the  oblique  meridian  St  L  S2; 
the  former  ray  (O  5X)  after  refraction  meets  the  first  focal  line 
at  Ix  and  the  second  focal  line  at  T2 ;  the  other  ray  0  S2 
meets  the  first  focal  line  at  I2  and  the  second  focal  line  at  7\. 
It  is  apparent  therefore  that  these  two  rays  never  meet  each  other 
after  their  refraction,  and  that  homocentric  rays  meeting  the 
asymmetrical  surface  in  a  common  oblique  meridian  cannot  be 
united  in  a  focus  by  this  refraction.  There  is  no  focus  in  any 
oblique  meridian. 

Image  of  a  Point  in  Asymmetrical  Refraction. — Since 
the  rays  proceeding  from  a  point  will  never  be  united  in  a  focus 
by  asymmetrical  refraction,  no  point  of  an  object  can  by  such 
refraction  be  reproduced  in  a  sharply  defined  image.  If  the  light 
proceeding  from  the  point  O  in  our  diagram  should  be  inter- 
cepted by  a  screen  at  Ex  the  image  of  the  point  would  be  a 
diffused  rectangle  of  light.  If  the  screen  were  placed  at  /  the 
image  would  be  a  vertical  line.  At  E  the  image  would  be  a 
square  and  at  T  it  would  be  a  horizontal  line. 

If  the  aperture  were  made  circular  as  in  the  ordinary  dia- 
phragm, the  image  at  /  and  at  T  would  not  be  altered,  but  at  Er 
and  E2  the  image  would  be  elliptical  and  at  E  it  would  be  a  circle. 

The  latter  is  called  the  circle  of  least  confusion. 

Image   of   a   Line    in   Asymmetrical    Refraction. — The 

image  of  a  vertical  line  passing  through  O  will,  as  projected  upon 

a  screen  at  I,  be  a  distinct  line,  for  each  point  of  the  line  will 

have  as  its  image  a  vertical  line,  such  as  7X  I2;  but  if  the  screen  is 

placed  at  T,  each  point  of  the  line  will  have  as  its  image  a  short 

horizontal  line,  as  T1  T2,  and  the  aggregation  of  all  these  lines 

will  make  a  broad  and  indistinct  line  as  the  image  of  the  vertical 

line.     At  any  other  point  the  image  of  the  vertical  line  will  be 

made  of  a  superposition  of  ellipses  or  circles. 


Refraction  at  Asymmetrical. Surfaces 


67 


The  image  of  a  horizontal  line  passing  through  0  will  be  the 
reverse  of  that  of  the  vertical  line ;  that  is,  the  image  will  be  a 
broad  and  indistinct  line  at  /  and  a  distinct  line  at  T. 

It  thus  appears  that  the  image  of  a  line  lying  in  one  principal 
meridian  will  be  distinct  at  the  focus  of  the  other  principal  meri- 
dian, and  most  indistinct  at  the  focus  of  the  meridian  in  which 
it  lies. 

The  image  of  a  line  lying  in  an  oblique  meridian  will  be 
blurred  in  all  positions  of  the  screen. 

The  Toric  Lens. — The  toric  curvature  of  a  lens  may  be 
convex  or  concave  as  shown  in  Fig.  38.  The  other  surface  of 
the  lens  may  be  plane  or  it  may  have  a  spherical  curvature  ground 
upon  it.  We  thus  have  in  the  toric  lens  a  combination  of  an 
asymmetrical  surface  with  a  surface  of  symmetry  such  as  we  have 
already  studied. 

The  Cylindrical  Lens. — The  cylindrical  curvature  differs 
from  the  curvature  of  a  toric  surface  only  in  that  the  former  has 
no  curvature  in  the  direction  of  the  axis  of  the  cylinder.  It  is 
in  fact  a  torus  in  which  the  radius  of  one  of  the  generating  circles 
is  infinite.  A  cylindrical  lens  is  bounded  on  one  face  by  a  cylin- 
drical curvature  and  on  the  other  by  a  plane  surface,  which  is 
parallel  to  the  axis  of  the  cylinder  (Fig.  40).    The  line  V  V  which 


fig.  40 

Refraction  by  a  Cylindrical  Lens 


passes  through  the  middle  of  the  lens  in  a  direction  parallel  to  the 
axis  of  the  cylinder,  is  called  the  axis  of  the  lens. 

In  the  refraction  by  a  cylindrical  lens  (or  cylinder,  as  it  is 
often  called)  there  is  no  refraction  of  rays  in  the  direction  of  the 


68  Principles    of    Optics 

axis  of  the  lens.  This  is  because  in  this  direction  the  two  faces  of 
the  lens  are  parallel.  As  this  axis  represents  one  principal  meri- 
dian of  the  lens,  the  entire  refractive  action  occurs  in  the  other 
principal  meridian,  which  is  at  right  angles  to  the  axis  of  the  lens. 

Notation  of  Toric  and  Cylindrical  Lenses. — These  lenses 
are  measured  in  terms  of  the  diopter,  which  is  used  for  the 
measurement  of  spherical  lenses.  In  denoting  the  strength  of  a 
toric  lens  we  express  the  dioptric  strength  in  the  two  principal 
meridians.  Thus  a  convex-toric  lens  having  a  refractive  power  of 
6  D  in  one  principal  meridian  and  of  8  D  in  the  other  would  be 
designated  as  -f  6  D,  -f  8  D. 

In  a  cylindrical  lens  the  dioptric  marking  denotes  the  re- 
fractive power  of  the  lens  in  its  refracting  meridian. 

Combination  of  Cylindrical  Lenses. — i .  The  combination 
of  tzvo  cylindrical  lenses  whose  axes  are  parallel  differs  in  nowise 
from  the  combination  of  two  spherical  lenses ;  the  combined  lenses 
are  equivalent  to  a  single  lens  whose  refracting  power  is  equal  to 
the  sum  of  the  powers  of  the  two  lenses. 

2.  Two  combined  cylindrical  lenses  whose  axes  are  at  right 
angles  are  equivalent  to  a  toric  lens.  If,  for  instance,  the  axis  of 
one  lens  is  vertical  and  that  of  the  other  is  horizontal,  the  first 
lens  refracts  the  rays  in  the  horizontal  and  the  second  refracts 
them  in  the  vertical  meridian,  just  as  they  are  refracted  in  the 
two  principal  meridians  of  the  toric  lens. 

In  a  bicylindrical  lens  one  curvature  must  be  ground  on  each 
face,  so  that  all  the  rays,  after  receiving  the  refractive  effect  of 
the  first  curvature,  may  also  receive  that  of  the  second  curvature. 
If  we  wish  to  grind  both  curvatures  upon  one  surface  we  must 
bear  in  mind  that  the  second  curvature  must  be  superposed  upon 
the  first  without  destroying  it;  we  must,  in  effect,  bend  the  axis 
of  the  first  cylinder  into  the  curvature  of  the  second  cylinder,  and 
we  see  that  in  so  doing  we  convert  the  surface  into  a  torus. 

If  both  cylinders  have  the  same  curvature  the  equivalent 
toric  curvature  becomes  spherical,  and  the  combined  effect  of 
two  equal  cylindrical  lenses  whose  axes  are  at  right  angles  is 
identical  with  that  of  a  spherical  lens  having  the  same  radius  and 
index. 

Since  two  unequal  cylindrical  lenses,  combined  at  right 
angles  to  each  other,  may  be  regarded  as  two  equal  lenses  so  com- 
bined with  the  addition  of  another  cylindrical  lens,  it   follows 


Refraction  at  Asymmetrical  Surfaces  69 

that  such  a  combination  is  equivalent  in  effect  to  a  spherical  lens 
combined  with  a  cylindrical  lens.  Thus  the  refractive  effect  is 
identical  whether  the  two  curvatures  are  ground  as  a  toric,  a 
bicylindrical,  or  a  sphero-cylindrical  lens. 

3.  Two  cylindrical  lenses  may  be  combined,  having  their 
axes  inclined  at  an  oblique  angle.  In  this  case  the  two  axes  of  the 
lenses  do  not  indicate  the  directions  of  the  principal  planes  or 
meridians  of  refraction  in  the  combination;  for  the  second  lens, 
not  being  at  right  angles  to  the  first,  deviates  the  rays  out  of  the 
plane  of  the  axis  of  the  first  lens,  and  vice  versa.  One  would, 
however,  naturally  suppose  that  there  must  be  in  such  a  com- 
bination a  certain  meridian  in  which  the  effect  of  the  combined 
refractions  is  greatest,  and  at  right  angles  to  this  another  in 
which  the  effect  is  least.  It  can,  in  fact,  be  demonstrated  that 
this  is  so  whatever  may  be  the  angle  of  inclination  of  the  axes ; 
that  any  two  obliquely  inclined  cylindrical  levises  in  combination 
are  equivalent  to  two  other  cylindrical  lenses  at  right  angles,  or 
to  the  equivalent  of  this — a  sphero-cylindrical  or  toric  lens. 

Perhaps  more  convincing  to  the  student  than  the  mathe- 
matical demonstration  (which  is  somewhat  complicated)  is 
practical  experiment  with  the  trial  lenses.  Selecting  any  two 
cylindrical  lenses  from  the  case  of  trial  lenses,  and  placing  them 
together  at  any  angle,  we  view  through  the  lenses  (which  are 
held  before  the  eye)  two  straight  lines  at  right  angles  to  each 
other,  as  the  edges  of  a  test-card.  These  lines  will,  in  general, 
appear  to  be  twisted  out  of  their  proper  relations ;  but  by  rotating 
the  combined  lenses  a  certain  position  can  always  be  found  in 
which  the  two  lines  appear  (as  they  are  in  reality)  at  right  angles 
to  each  other.  In  this  case  the  two  lines  viewed  mark  the  direc- 
tions of  the  principal  meridians,  and  the  combination  is  equivalent 
to  a  certain  toric,  or  sphero-cylindrical,  or  bicylindrical  lens  hav- 
ing these  principal  meridians.  The  nearest  equivalent  to  this 
combination  which  is  to  be  found  in  the  trial  case  may  be  ascer- 
tained by  neutralization — a  process  which  will  be  subsequently 
described. 

Asymmetry  of  Oblique  Refraction. — We  have  so  far 
confined  our  attention  to  direct  refraction,  in  which  the  axis  or 
medial  ray  of  the  pencil  of  light  meets  the  refracting  surfaces 
perpendicularly.  Strictly  speaking,  there  can  be  only  one  point 
of  an  object  from  which  a  direct  pencil  can  pass  through  a  lens 


jo  Principles    of    Optics 

or  system  of  refracting  surfaces.  This  point  is  the  point  of  inter- 
section of  the  optic  axis  and  the  object.  All  other  parts  of  the 
object  give  rise  to  indirect  or  oblique  pencils ;  but  when  the  object 
is  small  as  compared  with  its  distance  from  the  refracting  system, 
and  so  situated  that  its  central  point  lies  on  the  optic  axis,  the 
refractive  effect  differs  so  little  from  that  of  direct  pencils  that  we 
take  no  account  of  the  difference. 

In  the  refraction  by  the  eye  the  obliquity  of  pencils  may  be 
disregarded,  because  images  falling  upon  the  retina  at  a  con- 
siderable distance  from  the  optic  axis,  do  not  excite  in  the  mind 
a  distinct  visual  impression.  Tt  is  only  with  such  pencils  as  may 
be  regarded  as  direct  that  distinct  vision  is  concerned.  But 
in  vision  which  is  accomplished  with  the  aid  of  a  lens,  the  rays 
which  enter  the  eye  are  previously  obliquely  refracted  by  the  lens 
if  this  is  placed  in  a  tilted  position  before  the  eye. 

The  effect  of  the  oblique  position  of  the  lens  is  that  which 
results  from  spherical  aberration.  We  know  that  refraction  at 
a  spherical  surface  increases  with  the  obliquity  with  which  the 
rays  meet  the  surface.  We  see,  therefore,  that  if  we  intercept 
all  but  a  small  pencil  of  the  most  oblique  rays,  these  rays  will 
undergo  greater  refraction  than  the  central  rays  would  have 
undergone  if  they  had  not  been  intercepted,  and  that  if  there 
is  any  focus  for  these  oblique  rays,  it  must  lie  nearer  the  surface 
than  the  focus  for  the  central  rays,  that  is,  the  refractive  action 
is  more  powerful  for  the  oblique  than  for  the  direct  rays. 

The  mathematical  demonstration  of  what  actually  takes 
place  in  oblique  refraction  is  complicated,  but  by  examining  a 
lens  tilted,  as  in  the  vertical  meridian,  we  can  form  a  general 
idea  of  the  way  in  which  the  increase  of  refraction  occurs.  It  is 
easy  to  see  that  in  the  meridian  in  which  the  lens  is  tilted  the 
refractive  effect  must  be  increased  by  the  tilting,  but  it  requires 
closer  attention  to  see  that  the  effect  is  also  increased,  though  to 
a  less  extent,  in  the  meridian  at  right  angles  to  the  tilting. 

There  is,  therefore,  no  sharp  focus  for  rays  which  are  re- 
fracted with  considerable  obliquity,  but  if  we  take  into  consider- 
ation only  small  oblique  pencils,  we  may  assume  that  there  is 
a  focus  of  greatest  refraction  in  the  meridian  of  tilting  and 
another  focus  of  least  refraction  in  the  meridian  at  right  angles  to 
this  ;  or,  in  other  words,  we  may  for  our  purposes,  say  that  oblique 
refraction  is  similar  to  refraction  at  an  asymmetrical  surface. 


Refraction  at  Asymmetrical  Surfaces  Ji 

In  a  cylindrical  lens  the  refracting  power  in  the  direction 
of  the  axis  is  zero,  and  it  must  remain  so  when  the  lens  is  tilted. 
Tilting  a  cylindrical  lens,  therefore,  increases  its  power  in  its 
refracting  meridian ;  more  so  when  the  tilting  is  in  this  meridian. 

The  asymmetrical  effect  of  tilting  lenses  has  an  important 
bearing  in  the  combination  of  weak  cylindrical  with  strong 
spherical  lenses.  A  slight  amount  of  tilting,  as  is  almost  un- 
avoidable in  near  work,  may  either  entirely  neutralize  the 
cylindrical  effect  or  increase  it  beyond  what  is  desired. 

The  following  table  {Green)  shows  the  rate  of  increase  of 
a  lens  when  it  is  tilted  in  the  vertical  meridian : 

Degrees.  Vertical.        Horizontal. 

O 1.000  1.000 

5 I  .OIO  1 .002 

10 1042  I.OIO 

15 1.097  1-023 

20 1.179  IO4I 

25 1.297  1. 166 

45 2464  1232 

If  we  wish  to  find  the  asymmetrical  effect  produced  by  tilting 
a  lens  of  4  D,  for  instance,  fifteen  degrees  in  the  vertical  meri- 
dian, we  multiply  1.097  and  1-023  respectively  by  4.  This  gives 
us  4.388  D  as  the  refractive  effect  of  the  tilted  lens  in  the  vertical 
meridian,  and  4.092  D  in  the  horizontal  meridian.  The  difference 
.296  D,  represents  the  asymmetry  or  the  strength  of  the  cylindrical 
lens  which  would  be  required  to  equalize  the  two  meridians. 

Asymmetry  of  Prismatic  Refraction. — We  have  learned 
that  in  the  passage  of  light  through  a  prism  there  is  no  devia- 
tion of  rays  in  the  direction  of  the  base-apex  line  (or  axis)  of 
the  prism,  the  two  faces  of  the  prism  being  parallel  as  regards 
this  direction;  but  that  in  the  principal  plane  of  the  prism  the 
rays  are  all  deflected  towards  the  base  of  the  prism.  If  all  the 
rays  undergo  the  same  degree  of  deflection,  the  relative  direc- 
tion (the  divergence)  of  the  rays  will  be  unaffected.  This  is  the 
condition  which  exists  for  parallel  rays  and  approximately  for 
very  small  pencils  passing  through  the  prism  near  the  symmetrical 
ray;  but  other  pencils  have  their  relative  divergence  altered,  for 
the  pencils  are  altered  in  length  in  the  principal  plane  of  the 
prism  while  they  are  not  affected  in  the  direction  of  the  axis  of  the 
prism.     This  is  because  the  rays  which  are  most  removed  from 


72  Principles    of    Optics 

the  symmetrical  ray  are  more  deflected  than  the  rays  which  are 
near  this  position. 

Since  this  change  of  divergence  takes  place  in  the  principal 
plane  of  the  prism  but  not  in  the  direction  at  right  angles  to  this 
plane,  the  rays  which  diverge  from  a  point  will  lose  their 
homocentric  character,  and  the  refraction  is  comparable  to  that 
effected  by  an  asymmetrical  surface. 

The  study  of  refraction  by  prisms  becomes  still  more  com- 
plicated when  the  rays  do  not  lie  in  or  near  the  principal  plane, 
as  we  have  assumed,  for  rays  which  meet  the  principal  plane 
obliquely  undergo  greater  deviation  than  those  which  lie  in  this 
plane. 

But,  as  has  been  stated  in  a  previous  chapter,  we  assume  in 
ophthalmology  that  the  rays  are  all  equally  deviated,  and  that 
pencils  which  are  homocentric  before  entering  the  prism  remain 
so  after  passing  through  it.  It  is  therefore  only  necessary  that 
the  student  should  be  familiar  with  the  fact  that  this  assumption 
is  true  in  a  limited  sense,  so  that  he  may  be  able  to  understand 
the  distorting  effect  which  results  from  prismatic  refraction  under 
certain  conditions. 

The  following  authorities  have  been  consulted  in  the  prep- 
aration of  the  foregoing  chapter : 

Heath,  Geometrical  Optics. 

Prentice,  0 phtlialmic  Lenses. 

Sturm,  Sur  la  Theorie  de  la  Vision,  C.  R.  de  l'Acad.  de  Sci. 
de  Paris,  1845. 

Green,  Effect  of  Tilting  Lenses,  Trans.  Am.  Ophthal. 
Soc,  1890. 

Burnett,  Treatise  on  Astigmatism. 


CHAPTER   VI 


CORRECTION    OF   OPTICAL   DEFECTS   OF   THE   EYE 

BY    LENSES 

Spherical  lenses  have  been  used  for  the  improvement  of 
vision  for  a  very  long  time,  and  the  art  of  lens  making,  in  a 
crude  way,  dates  back  to  the  days  of  the  ancients.  What  is 
probably  the  oldest  lens  in  existence  is  a  convex  lens  of  crystal 
which  was  discovered  in  the  ruins  of  Nineveh,  and  is  now  in  the 
British  Museum  (Borsch). 

The  use  of  lenses  worn  as  spectacles,  supported  on  the  face 
by  frames,  dates  from  the  latter  part  of  the  thirteenth  century. 

Asymmetrical  lenses  were  introduced  by  Airy  in  the  early 
part  of  the  nineteenth  century,  but  it  was  not  until  after  the 
middle  of  that  century  that  they  came  into  general  use  with  the 
great  advance  made  in  the  study  of  the  refraction  of  the  eye 
by  Donders  and  his  collaborators.* 

Use  of  Spherical  Lenses 

In  order  that  rays  of  light  may  be  focused  on  the  retina  of  a 
hyperopic  eye  without  accommodation  these  rays  must  be  con- 


fig.  41 

vergent  when  they  enter  the  eye.  Thus  if  /  (Fig.  41)  is 
conjugate  to  R  on  the  retina,  rays  which  are  converging  to  / 
will  be  so  refracted  by  the  eye  as  to  be  focused  on  the  retina. 

•It  has  been  stated  that  priority  in  the  use  of  the  cylindrical  lens  belongs  to 
McAllister,  an  optician  of  Philadelphia,  in  that  he  corrected  a  case  of  astigmia  with 
such  a  lens  in  the  year  1825.  But  although  the  published  description  of  Airy's 
case  bears  the  date  of  1827,  he  presented  this  description  to  the  Cambridge  Philo- 
sophical Society  in  the  early  part  of   1825. 

(73) 


74 


Principles    of    Optics 


But  rays  proceeding  from  any  point  of  an  object  are  never 
convergent — they  are  divergent,  or  if  the  point  is  remote  they 
may  be  regarded  as  parallel.  We  must  therefore  for  the  correc- 
tion of  hyperopia  render  convergent  these  divergent  or  parallel 
rays  before  they  enter  the  eye.  We  do  this  by  means  of  a 
convex  spherical  lens  placed  before  the  eye.  The  parallel  rays 
proceeding  from  a  distant  point  would  be  focused  by  the 
hyperopic  eye  at  F'  behind  the  eye,  but  before  reaching  the  eye 
they  are  refracted  by  the  lens  L.  Being  thereby  rendered  con- 
vergent, they  would  be  focused  at  /,  but  before  reaching  /  they 
are  refracted  by  the  eye  and  are  focused  at  R  on  the  retina. 

Since  the  point  /  is  the  focusing  point  for  parallel  rays  in 
the  refraction  by  the  lens,  I  L  is  the  focal  length  of  the  lens 
which  corrects  the  hyperopia. 

The  lens  which  corrects  the  eye  for  parallel  rays  places 
the  eye  in  the  same  status  as  the  emmetropic  eye  for  focusing 
divergent  rays;  that  is,  this  eye  can  then  focus  divergent  rays 
on  the  retina  by  the  aid  of  accommodation.  If  the  latter  is  un- 
available or  insufficient,  a  stronger  lens  must  be  used  for  near 
work. 

In  emmetropia  or  corrected  ametropia  parallel  rays  can  be 
focused  on  the  retina,  but  if  the  crystalline  lens  is  unable  to 
undergo  an  increase  of  convexity  for  the  focusing  of  divergent 
rays  from  a  near  point,  a  convex  lens  must  be  used  for  near 
vision.  By  means  of  the  convex  lens  divergent  rays  are  made 
parallel  so  that  they  can  be  focused  on  the  retina.  This  use 
of  the  convex   lens   is   illustrated   in   Fig.   42.      Since    O   is   the 


fig.  42 


principal  focus  of  the  lens  L,  we  may  take  the  focal  length  0  L 
as  the  measure  of  the  accommodation  required  to  adapt  the  eye 
for  an  object  at  the  distance  of  O  from  the  eye.  If  for  instance 
O  is  25  cm  from  the  lens,  this  being  placed  at  a  standard  position, 
^—  gives  4  D  as  the  accommodation  required. 


Correction  of  Optical  Defects  of  the  Eye  by  Lenses        75 

When  some  accommodative  power  remains,  but  an  insuffi- 
cient amount  for  near  work,  a  weaker  convex  lens  is  used,  such 
as  overcomes  only  a  part  of  the  divergence  of  the  rays. 

In  the  myopic  eye  (Fig.  43)  parallel  rays  from  a  distant 
point  would  be  focused  at  F' ,  in  front  of  the  retina,  but  before 
entering  the  eye  they  encounter  the  concave  lens,  L,  and  are  so 


fig.  43 

refracted  that  they  now  appear  to  diverge  from  /,  which  is  con- 
jugate to  R  in  the  refraction  by  the  eye.  Therefore  a  concave 
lens  whose  focal  length  is  I  L  will  correct  the  myopia. 

Far  Point  of  the  Eye. — The  point  /,  which  is  conjugate 
to  R  on  the  retina,  is  called  the  far  point  {punctum  renwtum, 
p.  r.)  because  it  is  the  farthest  point  of  distinct  vision;  the 
image  of  any  more  distant  point  will  lie  in  front  of  the  retina. 
In  hyperopia  the  far  point  lies  behind  the  eye,  that  is,  the  far 
point  is  negative. 

Effect  of  Changing  the  Position  of  the  Correcting 
Lens. — When  a  convex  lens  is  placed  before  the  eye  in  order  to 
cause  the  image  of  an  object  (0,  Fig.  41*  )  to  fall  upon  the  retina, 
O  and  /  are  conjugate  points  in  the  refraction  by  the  lens.  These 
two  points  are  fixed,  but  the  lens  may  have  any  position  between 
A  and  O.  It  may  be  proved,  both  experimentally  and  mathe- 
matically, that  for  any  lens  the  line  0  I  between  conjugate  points 
is  shorter  when  the  lens  occupies  a  midway  position  between 
these  points  than  in  any  other  position.  Conversely,  for  the  fixed 
points  O  and  /  a  weaker  lens  will  suffice  when  this  is  placed 
midway  between  O  and  /  than  in  any  other  position. 

When  the  lens  occupies  this  midway  position  the  two  con- 
jugate focal  distances  O  L  and  /  L  are  each  equal  to  twice  the 
focal  length  of  the  lens.  Hence,  it  is  apparent  that  increasing 
the  distance  between  the  eye  and  the  lens  increases  the  correct- 
ing power  of  a  convex  lens  as  long  as  the  distance  of  the  lens 
from    the   object    is   more   than   twice   the    focal    length   of    the 


*The    conjugate    point    O    in    this    diagram    is    supposed    to    be    so    remote    that    its 
position  on  the  axis  cannot  be  represented. 


?6  Principles    of    Optics 

lens,  and  that  when  this  distance  is  less  than  twice  the  focal 
length  of  the  lens,  increasing  the  distance  between  the  eye  and 
lens  diminishes  the  correcting  power  of  the  latter. 

In  the  adaptation  of  the  hyperopic  eye  for  distant  vision  the 
distance  of  the  lens  from  the  object  is  more  than  twice  the  focal 
length  of  the  lens ;  consequently,  a  lens  which  corrects  the 
hyperopia  in  one  position  will  be  too  strong  or  too  weak  accord- 
ing as  it  is  moved  away  from  or  towards  the  eye ;  but  when  the 
object  is  near  the  lens,  as  in  the  use  of  reading  glasses,  the 
distance  between  the  object  and  the  lens  is  usually  less  than  twice 
the  focal  length,  and  a  change  in  position  of  the  lens  has  the 
opposite  effect — that  is,  a  stronger  lens  will  be  required  when  the 
distance  of  the  lens  from  the  eye  is  increased. 

Since  this  is  true,  we  are  confronted  with  the  question  as 
to  the  reason  for  the  common  belief  that  presbyopes  whose 
glasses  are  too  weak  acquire  the  habit  of  moving  them  off  to  the 
tip  of  the  nose  in  order  to  see  more  distinctly.  If  this  device 
does  render  vision  better  it  is  probably  because  of  the  attendant 
obliquity  of  the  lenses,  whereby  the  refractive  power  is  increased, 
but  with  the  disadvantage  of  an  induced  asymmetry  of  action. 

In  the  concave  lens,  the  focal  distance  being  negative,  the 
distance  between  the  object  and  lens  is  (algebraically)  always 
less  than  twice  the  focal  length ;  consequently,  a  stronger  concave 
lens  is  always  required  when  the  distance  of  the  lens  from  the 
eye  is  increased.    This  is  apparent  from  inspection  of  Fig.  43. 

Measurement  of  Ametropia  by  the  Correcting  Lens. — 
The  degree  of  ametropia  may  be  conveniently  measured  by  the 
lens  required  to  focus  the  image  of  a  distant  object  upon  the 
retina ;  but  since  the  strength  of  this  lens  varies  with  its  distance 
from  the  eye,  it  is  necessary  to  adopt  a  standard  position  at  which 
the  measuring  lens  is  to  be  placed.  For  this  purpose  it  is  cus- 
tomary to  regard  the  lens  as  placed  at  a  distance  of  15  mm  from 
the  eye.     This  is  approximately  at  the  anterior  focus. 

Effect  of  Lenses  upon  the  Size  of  Retinal  Images. — 
In  general,  a  lens  placed  before  the  eye  alters  the  size  of  the 
retinal  image ;  but  spectacle-lenses,  owing  to  the  fact  that  they 
are  worn  very  near  the  anterior  focus  of  the  eye,  usually  produce 
only  a  slight  modification  in  this  respect. 

The  effect  of  placing  a  convex  lens  at  the  anterior  focus  of 
the  eye  is  illustrated  in  Fig.  44,  in  which  A  represents  the  re- 


Correction  of  Optical  Defects  of  the  Eye  by  Lenses        yj 

fracting  surface  of  the  reduced  eye.     We  have  learned  that,  in 
estimating  the  size  of  images,  the  interval  between  the  principal 


fig.  44 

points  may  be  disregarded;  hence,  if  A  F  and  A  F'  represent  the 
anterior  and  posterior  focal  distances  of  the  eye,  /  Ix  will  represent 
the  image  of  the  object  0  Ox  in  the  refraction  by  the  eye  alone. 
If  the  image  /  /,  lies  behind  the  retina  R  Rlf  it  may  be  brought 
forward  by  a  convex  lens.  When  this  lens  is  placed  at  the  anterior 
focus,  as  illustrated  in  Fig.  44,  the  ray  0{  F,  passing  through  the 
anterior  focus,  passes  also  through  the  nodal  point  of  the  lens; 
consequently,  its  direction  is  unaltered  by  the  lens,  and  the  image 
R  i?x  on  the  retina  has  the  same  size  as  /  Ix,  formed  by  the  eye 
without  the  aid  of  the  lens. 


fig.  45 


When  the  convex  lens  is  without  the  anterior  focus,  the 
image  is  not  only  brought  forward,  but  it  is  at  the  same  time 
enlarged,  as  is  shown  in  Fig.  45. 


fig.  46 

When  the  convex  lens  is  within  the  anterior  focus  of  the 
eye  the  image  is  brought  forward,  but  it  is  diminished  in  size,  as 
is  shown  in  Fig.  46*. 

•These  diagrams,  illustrative  of  special  conditions,  do  not  afford  a  general 
demonstration;  but  it  can  be  proved  algebraically  that  for  all  relations  of  conjugate 
foci  images  are  affected  in  the  same   way  as  in  these  illustrations. 


yS  Principles    of    Optics 

The  effect  of  a  concave  lens  is  opposite  to  that  of  a  con- 
vex lens.  A  concave  lens  at  the  anterior  focus  of  the  eye  moves 
the  image  backward  without  changing  its  size.  When  the  lens 
is  without  the  anterior  focus  the  image  is  made  smaller,  and  when 
the  lens  is  within  the  focus  the  image  is  enlarged. 

We  see,  therefore,  that  we  cannot  properly  illustrate  the 
effect  of  lenses  used  in  the  correction  of  ametropia  by  means  of 
the  enlargement  of  the  virtual  image  of  the  convex  lens,  or  by 
the  minification  of  the  virtual  image  of  the  concave  lens.  An 
actual  enlargement  or  diminution  in  size  occurs  according  as 
the  lens  in  combination  with  the  eye  produces  a  larger  or  smaller 
image  than  does  the  eye  alone. 

When  a  convex  lens  is  used  as  a  "magnifying  glass"  the  conditions 
are  somewhat  different  and  further  explanation  is  required.  The 
action  of  a  lens  used  as  a  magnifier  or  simple  microscope  is  shown 
in   Fig.   47.     Although   the   lens   may   be   at   or   near   the   anterior   focus 


fig.  47 

of  the  eye,  the  object  A  B  will  be  seen  with  magnification.  This  is 
because  the  lens  enables  us  to  focus  on  the  retina  the  rays  from  the 
object  when  this  is  placed  very  near  the  eye.  If  we  could  focus  rays 
coming  from  the  object  situated  equally  near  the  eye  without  the  aid 
of  the  lens  we  would  see  it  with  as  much  enlargement  as  we  do  with  the 
lens.  But  it  is  only  with  the  lens  that  rays  from  so  near  an  object  are  focused 
on  the  retina,  and  as  we  are  not  accustomed  to  seeing  clearly  objects  placed 
so  near  the  eye,  we  unconsciously  regard  an  object  so  seen  as  being  at 
a  greater  distance  and  as  having  a  proportionately  greater  size. 

In  the  use  of  a  convex  lens  for  this  purpose  the  object  to  be  magnified 
is  placed  at  or  near  the  principal  focus  of  the  lens.  When  the  observer's 
eye  is  emmetropic  and  he  uses  no  accommodation  the  object  is  at  the 
principal  focus  so  that  the  rays  from  the  object  will  be  parallel  when 
they  enter  his  eye.  If  he  is  hyperopic,  he  will  need  to  have  the  rays 
rendered  slightly  convergent  so  that  he  can  focus  them  without  accommo- 
dation, and  the  object  must  be  without  the  principal  focus.  On  the 
other  hand,  if  he  is  myopic,  the  object  must  be  within  the  principal 
focus  so  that  the  rays  will  enter  his  eye  in  divergent  pencils. 


Correction  of  Optical  Defects  of  the  Eye  by  Lenses        79 

We  have  learned  that  the  position  of  greatest  efficiency  of  a  convex 
lens  is  midway  between  the  two  conjugate  foci  and  that  moving  it  away 
from  the  eye  and  towards  the  object  diminishes  its  power  when  by  so 
moving  it  we  carry  it  farther  from  the  midway  position.  The  same  is  true 
of  the  magnifying  power  of  a  convex  lens  used  in  combination  with  the 
eye,  and  any  further  movement  of  the  lens  towards  the  object  diminishes 
the  magnifying  power.  Practically  we  must,  however,  continue  to  move 
the  lens  towards  the  object  until  the  image  on  the  retina  becomes  clear 
which  (as  has  just  been  shown)  is  when  the  object  is  near  the  principal 
focus  of  the  lens.  This  is  the  position  of  greatest  magnifying  power 
and  any  further  movement  of  the  lens  towards  the  object  diminishes 
the  magnification. 

In  hyperopia  distinctness  of  vision  is  attained  by  accom- 
modative action,  whereby  the  focal  distances  of  the  eye  are 
shortened  and  images  are  reduced  in  size.  By  the  substitution 
of  a  convex  lens  placed  at  the  anterior  focus  the  accommodation 
is  relaxed,  the  focal  distances  resume  their  normal  dimensions, 
and  images  are  proportionately  enlarged. 

When  the  lens  is  worn  without  the  anterior  focus,  there  is 
additional  enlargement  due  to  the  magnifying  power  of  the  lens. 
Even  in  high  hyperopia,  however,  the  difference  in  size  of  images 
without  lens-correction  and  with  it  is  not  great.  The  difference 
is,  nevertheless,  appreciable,  for  it  is  possible  to  discern  very 
slight  changes  in  the  dimensions  of  the  stimulated  retinal  area. 

Similarly,  when  convex  lenses  are  used  as  reading  glasses, 
these  being  necessitated  by  failure  of  accommodation,  retinal 
images  are  slightly  larger  than  when  the  focal  distances  are 
shortened  by  accommodative  action. 

In  myopia  distinct  distant  vision  is  impossible  without  a  cor- 
recting lens.  When  the  myopia  is  due  to  axial  elongation  (the 
focal  distances  being  normal),  the  proper  concave  lens  placed  at 
the  anterior  focus  of  the  eye  brings  the  image  to  a  focus  on  the 
retina  without  changing  its  size,  that  is,  the  image  has  the  same 
size  as  it.  would  have  in  emmetropia.  If  the  correcting  lens  is 
worn  without  the  anterior  focus  of  the  eye,  the  image  is  smaller 
than  in  emmetropia. 

Enlargement  of  Images  Effected  by  Removal  of  the 
Crystalline  Lens. — In  aphakia  the  anterior  focal  distance  is 
greater  than  that  of  the  schematic  eye  in  the  proportion  of 
about -23  to  16.  Since  images  are  proportional  to  the  anterior 
focal  distance,  they  must  be  larger  after  removal  of  the  lens  than 
they  are  in  the  normal  eye.  However,  if  the  axial  length  of  the 
eye  is  normal,  images  as  formed  by  the  aphakic  eye  will  lie  far 


80  Principles    of    Optics 

behind  the  retina,  and  distinct  vision  can  be  obtained  only  with 
the  aid  of  a  strong  convex  lens.  This  lens,  if  worn  as  an  eye- 
glass, will  be  within  the  anterior  focus  of  the  eye  in  its  aphakic 
condition,  and  consequently  it  will  reduce  the  size  of  images,  so 
that  they  will  more  nearly  correspond  to  those  of  the  normal  eye. 

It  is  in  extreme  axial  elongation  (high  myopia)  that  the 
enlargement  of  images  resulting  from  removal  of  the  lens  is 
most  noticeable.  If  the  elongation  is  so  great  that  the  posterior 
principal  focus  falls  on  the  retina  of  the  eye  after  its  lens  has 
been  removed,  the  image  of  a  distant  object  will  be  clearly 
formed  on  the  retina  without  any  correcting  lens.  Each  linear 
dimension  of  the  object  as  thus  formed  will  be  about  one  and 
one-half  times  as  large  as  with  the  concave  correcting  lens 
which  was  required  before  removal  of  the  lens. 

Length  of  Axis  in  Ametropia. — If  we  may  assume  with- 
out error  in  any  case  of  hyperopia  or  myopia  that  the  curvatures, 
indices,  and  intervals  between  the  surfaces  do  not  differ  materially 
from  those  of  the  schematic  eye,  the  degree  of  ametropia,  as 
measured  by  the  correcting  lens,  affords  a  means  of  estimating 
the  deficiency  in  length  of  the  eye  in  hyperopia  or  the  excess  of 
length  in  myopia. 

For  this  purpose  we  use  the  equation 

F  F/ 

I      ' 

in  which  /  is  the  distance  of  the  far  point  (/,  Fig.  41)  from  the 
anterior  focus,  and  ?  is  the  distance  of  the  retina  from  the 
posterior  focus. 

In  the  application  of  this  formula  to  myopia  of  10  D,  as 
measured  by  the  correcting  lens  placed  at  the  anterior  focus, 
I  =  100  mm.  By  substituting  for  F  (15.76)  and  for  F'  (21.07) 
their  values,  we  derive  3.3  mm,  as  the  corresponding  value  of  /'. 
Since  this  is  the  distance  of  the  retina  behind  the  principal  focus, 
it  is  the  excess  of  axial  length  for  10  D  of  myopia. 

In  hyperopia  of  10  D,  as  measured  by  the  correcting  lens 
placed  at  the  anterior  focus  of  the  eye,  /,  being  negative  is 
—  100  mm  and  by  the  substitution  of  this  value  we  find  that  /'  is 
equal  to  —  3.3  mm,  which  shows  that  in  10  D  of  hyperopia  the 
deficiency  in  axial  length  is  3.3.  mm. 


Correction  of  Optical  Defects  of  the  Eye  by  Lenses        81 

The  deficiency  in  length  of  the  hyperopic  eye  is  equal  to  the 
excess  in  the  same  degree  of  myopia,  when  these  conditions  are 
measured  by  the  correcting  lens  placed  at  the  anterior  focus  of 
the  eye. 

Each  millimeter  of  deficiency  or  excess  of  length  cor- 
responds to  three  diopters  of  ametropia. 

Axial  Length  of  the  Eye  in  Relation  to  the  Probable 
Refractive  Condition  after  Removal  of  the  Lens. — We 
may  make  use  of  the  same  equation  (I  I'  =  F  F')  to  determine 
the  probable  refractive  condition  after  removal  of  the  lens  from 
the  eye. 

In  the  application  of  this  formula  to  an  eye  which  is 
emmetropic  before  removal  of  the  lens,  and  in  which  therefore 
the  axial  length  is  presumably  about  23.22  mm,  IF  (IF  =1  L, 
Fig.  41 )  is  denoted  by  /,  and  R  F'  is  denoted  by  —  /'.  The  minus 
sign  is  used  because  R  lies  on  the  left  of  F'.  In  this  equation 
F  and  F'  represent  respectively  the  anterior  focal  distance  (  A  F) 
and  the  posterior  focal  distance  (A  F')  of  the  aphakic  eye.  The 
first  of  these  distances  is  23.14  mm,  and  the  second  is  30.94  mm 
(average  measurements).  We  observe  also  that  R  F'  is  equal 
to  the  difference  between  A  F'  (30.94  mm)  and  A  R  (23.22' 
mm),  or  R  F'  =  I'  =  —  7.72  mm. 

By  substitution  of  the  values  of  F  and  F'  we  have  the 
equation, 

—  7.72  I  =  30.94  X  23.14 

From  this  we  find  /  =  —  93  mm. 

This  means  that  93  mm  is  the  focal  length  of  the  lens  which 
is  required  to  correct  the  hyperopia  after  removal  of  the  lens, 
if  the  correcting  lens  is  placed  at  the  anterior  focus  of  the  aphakic 
eye;  but  this  focus  is  about  2^  mm  from  the  cornea,  a  greater  dis- 
tance than  that  at  which  correcting  lenses  are  worn.  We  there- 
fore subtract  8  mm,  in  order  to  reduce  the  distance  to  the 
standard  which  we  have  assigned  as  the  position  of  correcting 
lenses,  and  this  gives  85  mm  as  the  focal  length  of  the  correct- 
ing lens. 

A  focal  length  of  85  mm  corresponds  to  a  dioptric  power  of 
1 1.7  D,  which,  therefore,  is  theoretically  the  degree  of  hyperopia 
to  be  overcome  after  removal  of  the  crystalline  lens  from  an 
emmetropic  eye. 


82  Principles    of    Optics 

Since  individual  eyes  differ  more  or  less  from  the  schematic 
eye  in  their  measurements,  we  must  not  suppose  that  the  lens 
as  practically  determined  will  correspond  exactly  with  that  here 
derived  by  calculation.  As  a  matter  of  fact  the  lens  so  derived 
seems  to  be  slightly  stronger  than  is  usually  required  after  re- 
moval of  the  crystalline  lens  from  an  eye  which  was  known  to 
have  been  emmetropic  before  the  formation  of  cataract.  As  a  rule 
a  lens  of  10  D  or  at  most  n  D  suffices  to  correct  the  hyperopia 
of  such  an  eye. 

In  other  refractive  conditions  the  same  method  may  be  used 
to  determine  the  probable  strength  of  the  lens  which  will  be 
required  to  correct  the  ametropia  after  removal  of  the  crystalline 
lens.  The  only  difference  between  this  and  the  foregoing  pro- 
cedure is  that  instead  of  the  distance  A  R  being  equal  to  23.22 
tiim,  the  length  of  the  emmetropic  eye,  its  value  must  be  assigned 
in  accordance  with  the  degree  of  ametropia. 

A  condition  of  practical  interest  is  that  in  which  the  eyeball 
has  undergone  great  elongation  with  a  resulting  high  degree  of 
myopia.  We  may  then  wish  to  know  whether  such  an  eye  will 
be  myopic,  emmetropic,  or  hyperopic  after  removal  of  the  lens. 

The  posterior  focus  of  the  aphakic  eye  of  normal  curvature 
and  index,  lies,  as  we  have  already  learned,  about  31  mm  behind 
the  anterior  surface  of  the  cornea.  If,  therefore,  the  myopic  eye 
is  so  elongated  that  the  retina  is  also  situated  at  this  distance 
from  the  cornea,  the  eye  will  be  adapted  to  focus  the  image  of  a 
distant  object  upon  the  retina  after  removal  of  the  crystalline 
lens. 

If  under  the  same  conditions  the  axial  length  is  more  than  31 
mm  the  eye  will  still  be  myopic  after  it  has  been  rendered 
aphakic;  but  if  the  axial  length  is  less  than  31  mm,  the  aphakic 
eye  will  be  hyperopic. 

An  axial  length  of  31  mm  corresponds  to  myopia  of  about 
23  D,  as  measured  by  the  correcting  lens  at  the  anterior  focus  of 
the  eye,  and  this  is  therefore  the  degree  of  axial  myopia  which 
must  exist  under  average  conditions  in  order  that  the  eye  may 
be  emmetropic  after  removal  of  its  crystalline  lens.  Practically 
it  has  been  found  by  those  who  have  removed  the  crystalline  lens 
for  the  improvement  of  vision  in  high  myopia  that  emmetropia 
(or  a  condition  approximating  this)  may  result  in  myopia  of 
various  degrees,  between  eighteen  and  twenty-five  diopters. 


Correction  of  Optical  Defects  of  the  Eye  by  Lenses        83 

Correction  of  Astigmia 

There  are  two  kinds  of  astigmia :  regular  and  irregular. 
The  former  is  due  to  asymmetrical  curvature  of  the  cornea  or 
crystalline  lens.  The  latter  arises  from  irregularity  or  uneven- 
ness  of  surface,  or  from  heterogeneity  of  structure.  Our 
attention  is  here  confined  to  regular  astigmia,  which  is  always 
signified  by  the  term  astigmia  unless  it  is  otherwise  stated. 

By  referring  to  our  diagram  of  asymmetrical  refraction 
(Fig.  39)  we  see  that  if  we  place  a  cylindrical  lens  in  front  of 
the  surface  so  that  it  increases  the  refraction  of  the  rays  in  the 
vertical  meridian  to  such  an  extent  as  to  change  the 
vertical  focus  from  T  to  /,  all  the  rays  from  0  must  then  meet 
in  the  point  /;  the  pencil  is  again  homocentric,  and  the  asym- 
metry is  overcome. 

So  also  if  we  make  use  of  a  concave  cylinder  so  placed  as 
to  change  the  horizontal  focus  from  I  to  T  the  rays  will 
meet  in  the  point  T.  In  this  case  as  well  as  in  the  former  the 
astigmia  is  overcome. 

Astigmia  is  therefore  corrected  by  any  lens  that  will 
equalize  the  refraction  of  the  eye  in  the  two  principal  meridians. 
If  the  retina  were  at  the  focus  /,  we  should  use  the  convex  lens 
with  its  axis  horizontal,  while  if  the  retina  were  at  T  we  should 
use  the  concave  cylinder  with  vertical  axis.  But  when,  as  is 
often  the  case,  the  retina  coincides  with  neither  focus,  we  must 
add  a  spherical  lens  to  the  astigmia  correction  so  as  to  bring 
the  rays  which  are  rendered  homocentric  by  the  cylinder  to  a 
proper  focus  on  the  retina. 

Distortion  of  Images  in  Astigmia. — In  investigating  the 
form  of  images  in  astigmia  we  must  consider  both  the  blurred 
image  as  formed  without  the  correcting  lens  and  the  focused 
image  as  formed  with  the  aid  of  the  lens. 

Since  the  linear  dimensions  of  the  image  are  proportional 
to  the  anterior  focal  distance  of  the  eye  (p.  58).  and  since 
this  distance  is  greater  as  the  curvature  is  less,  it  is  clear  that 
the  image  as  formed  in  the  meridian  of  greatest  refraction  is  less 
than  that  formed  in  the  meridian  of  least  refraction.  The  retina 
cannot,  however,  be  in  position  to  receive  the  focused  image  in 
both  meridians  so  that  the  light  is  diffused  on  the  retina  in  the 
unfocused  meridian.     The  effect  of  diffusion  upon  the  apparent 


84 


Principles    of    Optics 


size  of  the  image  varies  with  the  size  of  the  pupil,  and 
with  the  relation  of  the  diffusion  to  the  magnification  or  minifi- 
cation  of  the  focused  image.  Generally  the  diffusion  on  the 
retina  makes  the  image  appear  too  large  in  the  unfocused  meri- 
dian whether  this  is  hyperopic  or  myopic. 

When  the  astigmia  is  corrected  by  a  lens  at  the  anterior 
focus  of  the  faulty  meridian,  the  image  may  be  focused  on  the 
retina ;  but  the  size  of  the  image  will  remain  the  same  as  it  would 
be  as  formed  at  its  focus  without  the  lens.  In  other  words  the 
corrected  image  is  proportionally  too  large  in  the  meridian  of 
least  refraction  or  too  small  in  that  of  greatest  refraction.  If  the 
correcting  lens  is  worn  without  the  anterior  focus  the  distortion 
may  be  further  increased  by  the  magnifying  or  minifying  power 
of  the  lens. 

Owing  to  the  disproportion  of  the  image  in  astigmia1,  all 
lines  which   are   not   parallel   or   perpendicular   to   the   principal 


meridians  undergo  an  angular  distortion.  The  explanation  of 
this  is  given  in  Fig.  48,  in  which  O  A  and  O  B  indicate  the  di- 
rections of  the  principal  meridians,  O  B  being  that  in  which  the 
image  appears  too  large.  The  image  of  a  square  whose  sides  are 
obliquely  inclined  to  the  principal  meridians  would  not  be  the 
square  A  B  C  D  but  the  oblique  figure  A  Bt  C  Dly  for  there  is 


Correction  of  Optical  Defects  of  the  Eye  by  Lenses        85 

an  undue  magnification  in  the  direction  O  B,  so  that  5X  Dx  is  a 
longer  line  than  A  C.  Hence,  the  oblique  line  which  would 
normally  appear  as  A  B  appears  in  the  distorted  image  as  A  Bx, 
which  makes  a  greater  angle  with  A  O  than  A  B  does. 

The  degree  of  astigmia  in  the  eye  is  slight  as  compared 
with  the  total  refraction,  and,  consequently,  the  two  focal  lines 
are  very  near  each  other;  hence,  the  actual  distortion  either  with 
or  without  correction  is  not  great. 

Determination  of  the  Axis  of  a  Cylindrical  Lens. — 
When  a  cylindrical  lens  is  placed  before  the  eye  at  a  greater 
distance  than  that  at  which  spectacles  are  worn,  while  a  distant 


II 


III 


FIG.   49 


Determination  of  the  axis  of  a  cylinder.  A  right-angled  cross,  A  B  C  D,  is  seen 
through  a  glass  containing  a  cylinder.  If  (I)  the  axis  of  the  cylinder  does  not 
coincide  with  either  A  B  or  C  D  the  cross  will  appear  twisted,  so  that  the  arms  no 
longer  make  a  right  angle.  The  cross,  however,  is  not  displaced  as  a  whole  either 
to  one  side  or  the  other.  If  now  the  glass  is  rotated  until  the  axis  of  the  cylinder 
coincides  with  one  arm  of  the  cross — e.  g.,  A  B.  (II) — the  cross  will  appear  right- 
angled  and  unbroken.  The  same  thing  will  happen  if  the  glass  is  rotated  900  more 
(III),  so  that  the  axis  of  the  cylinder  coincides  with  C  D. 

object  is  viewed  through  the  lens,  the  distortion  may  become  very 
great.  This  property  is  used  for  the  ready  determination  of  the 
direction  of  the  axis  of  a  cylindrical  lens.  To  find  the  position 
of  the  axis  we  hold  the  lens  before  the  eye  and  look  through  it 
at  a  straight  line  across  the  room,  as  the  edge  of  a  test-card, 
rotating  the  lens  in  its  own  plane  until  we  reach  that  position  in 
which  there  is  no  break  in  the  line,  as  seen  through  the  lens  and 
beyond  its  border  (Fig.  49).    The  axis  is  then  either  parallel  or 


86  Principles    of    Optics 

perpendicular  to  the  line.  If  the  length  of  the  line  is  unaffected  by 
the  lens  it  lies  in  the  direction  of  the  axis,  but  if  it  is  magnified 
or  minified  in  length  it  lies  at  right  angles  to  the  axis;  or  if  a 
movement  of  the  lens  in  the  direction  of  the  line  does  not  affect 
the  apparent  position  of  objects  the  line  lies  in  the  direction 
of  the  axis,  but  if  such  movement  produces  apparent  displace- 
ment the  line  is  at  right  angles  to  the  axis.  If  the  displacement 
is  in  the  opposite  direction  to  that  of  the  lens,  or  if  an  oblique 
line  appears  to  make  a  greater  angle  with  the  axis  than  really 
exists,  the  lens  is  convex;  if  the  displacement  is  in  the  direction 
of  motion  of  the  lens,  or  if  an  oblique  line  appears  to  make 
a  less  angle  with  the  axis  than  really  exists,  the  lens  is  concave. 

The  following  authorities  have  been  consulted  in  the  prepara- 
tion of  the  foregoing  chapter : 

Borsch,  Lens,  Encyclopaedia  Americana. 
Airy,    On  a  Peculiar  Defect  in  the  Eye  and  a  Mode  of  Cor- 
recting it,  Trans.  Camb.  Philos.  Soc,  1827. 
Burnett,  Treatise  on  Astigmatism. 
Heath,  Geometrical  Optics. 

Donders,  Anomalies  of  Refraction  and  Accommodation. 
Landolt,  Refraction  and  Accommodation  of  the  Eye. 
Duane,  Refractive  Errors,  in  Posey's  Diseases  of  the  Eye. 


CHAPTER  VII 


OPTICAL     PRINCIPLES     OF     OPHTHALMOSCOPY, 
SKIASCOPY,  AND  OPHTHALMOMETRY 

In  Fig.  50FP  represents  the  pupil  of  an  eye  under  exam- 
ination. Let  us  suppose  first  that  the  eye  is  myopic,  so  that 
O  and  /  are  conjugate  points,  as  are  also  Ox  and  Iv  and  02  and 


FIG.   50 

Illustrating  the  path  of  the  reflected  and  refracted  rays  in  indirect  ophthalmoscopy 
and  in  skiascopy.  The  rays  emerging  from  the  eye  (P  P)  undergoing  examination  are 
rendered  convergent  by  inherent  myopia  of  this  eye  or  by  a  convex  lens  placed 
in  front  of  the  eye. 

I2.  Light  from  a  point  L  is  reflected  into  the  eye  P  P  by  a  plane 
mirror  M  M.  The  rays  of  light  will  enter  the  eye  as  if  they  di- 
verged from  Lv  as  far  behind  the  mirror  as  L  is  in  front  of  it. 
Since  Lx  is  farther  than  the  conjugate  O  from  the  eye,  the  rays 
will  cross  in  front  of  the  retina,  and  will  form  on  the  latter  a 
diffusion  image  Ix  I2. 

Some  of  the  light  from  the  illuminated  area  7\  I2  undergoes 
irregular  reflection  and  passes  out  of  the  eye.  Of  the  light  thus 
reflected,  all  rays  which  proceed  from  /  must  intersect  at  O ;  all 
which  proceed  from  Ix  intersect  at  01;  and  all  which  proceed 
from  02  intersect  at  I2.  There  is  formed,  therefore,  at  Oj  02  a 
real  inverted  (aerial)  image  of  the  illuminated  portion  of  the 
fundus. 

(87) 


88  Principles    of    Optics 

If  the  flame  were  so  placed  that  the  light  entered  the  eye 
as  if  diverging  from  O,  conjugate  to  the  retina,  there  would 
be  no  diffusion  on  the  retina  but  a  focused  image  of  the  point  of 
light.  If,  on  the  other  hand,  the  rays  should  diverge  from  a' 
point  nearer  to  P  P  than  0,  they  would  reach  the  retina  before 
their  union  in  a  focus,  and  as  before  there  would  be  a  diffusion 
of  light  on  the  retina.  The  area  of  illumination  is  therefore 
greater  as  the  point  of  origin  of  the  light  is  more  removed  from 
the  conjugate  to  the  retina. 

It  is  only  in  myopia  that  a  real  image  of  the  illuminated 
area  will  be  formed  in  front  of  the  eye,  for  in  emmetropia  the 
emergent  rays  from  any  point  of  the  fundus  will  be  parallel, 
and  in  hyperopia  the  emergent  rays  will  be  divergent,  and  will 
appear  to  proceed  from  a  virtual  image  behind  the  eye. 

The  size  of  the  image  in  relation  to  the  size  of  the  illu- 
minated area  of  the  retina  depends  upon  the  respective  distances 
of  the  two  conjugates  from  the  nodal  point  of  the  eye.  Thus 
in  axial  myopia  of  10  D  the  image  is  situated  approxi- 
mately at  107  mm  from  the  nodal  point,  while  the  retina  is  about 
19  mm  from  this  point.  The  ratio  ±^-  gives  us  a  magnification 
of  about  5^2  diameters.  The  magnification  diminishes  with  the 
increase  of  myopia. 

But  the  emergent  rays  in  emmetropia  and  hyperopia  may  be 
united  in  a  real  aerial  image  in  front  of  the  eye  by  the  aid  of  a 
convex  lens.  The  position  of  the  image  will,  of  course,  depend 
upon  the  strength  of  the  lens  used.  The  convex  lens  may  also 
be  used  in  myopia  to  bring  the  image  nearer  to  the  eye  than  it 
would  be  as  formed  by  the  eye  alone. 

In  emmetropia  the  size  of  the  image  as  formed  by  the  con- 
vex lens  is  determined  by  the  ratio  of  the  anterior  focal  length 
of  the  eye  to  the  focal  length  of  the  lens,  irrespective  of  the 
position  of  the  lens.  In  axial  hyperopia  and  myopia  the  image 
has  the  same  size  as  in  emmetropia  when  the  focus  of  the  lens 
coincides  with  the  anterior  focus  of  the  eye.  When  the  lens  is 
nearer  than  this  the  image  is  greater  in  hyperopia  and  less  in 
myopia;  when  the  focus  of  the  lens  is  beyond  the  anterior  focus 
of  the  eye  the  image  is  smaller  in  hyperopia  and  greater  in  myopia. 

The  reason  that  the  pupil  of  the  eye  appears  black  under 
ordinary  conditions  and  that  we  do  not  see  the  illuminated  area 
of  the  fundus  is  that  we  have  to  place  our  head  in  such  position 


Ophthalmoscopy,  Skiascopy,  and   Ophthalmometry         89 

when  we  look  into  another  person's  eye  that  we  intercept  the 
light  which  would  illuminate  that  part  of  the  fundus  lying  in  our 
line  of  vision.  The  path  of  the  entering  rays  lies  very  near  that 
of  the  emerging  rays.  This  is  most  notably  true  in  emmetropia. 
In  hyperopia  the  rays  diverge  as  they  leave  the  eye,  and  in 
myopia  they  diverge  after  they  have  intersected  in  the  aerial 
image.  This  is  why  the  pupil  sometimes  is  seen  to  shine  in  high 
degrees  of  hyperopia  or  myopia. 

But  in  order  that  we  may  make  practical  use  of  the  emergent 
rays  for  examining  the  fundus  we  must  have  a  device  which 
will  allow  these  rays  to  enter  the  observer's  eye  without  interfering 
with  the  illumination  of  the  retina.  Although  Briicke  in  1847 
discovered  the  principles  on  which  ophthalmoscopy  is  founded, 
the  full  explanation  of  them  and  their  practical  application  by 
the  invention  of  the  ophthalmoscope  is  due  to  the  genius  of 
Helmholtz  (1851). 

The  ophthalmoscope  in  its  simplest  form  consists  of  a  plane 
or  concave  mirror  having  at  its  center  a  small  circular  opening, 
through  which  light  can  pass  to  the  eye  of  the  observer.  There 
must  also  be  attached  to  the  mirror  a  series  of  lenses  to  facilitate 
the  focusing  of  the  image. 

Although  the  ophthalmoscope  has  been  made  in  many  differ- 
ent forms,  the  principle  is  the  same  in  all.  It  is  therefore 
unnecessary  to  describe  the  various  stages  of  evolution  through 
which  this  invention  has  passed.  It  suffices  to  say  that  Helmholtz 
did  not  use  a  silvered  mirror,  as  we  do  now.  He  used  a  plate 
of  plane  glass,  which  reflected  light  into  the  eye  under  examina- 
tion and  at  the  same  time  permitted  some  of  the  emergent  rays  to 
pass  through  it  and  into  the  eye  of  the  observer.  We  know  that 
much  of  the  light  from  the  flame  would  pass  through  the  plate 
of  glass,  and  that  the  illumination  of  the  fundus  would  be  feeble. 
By  using  several  plates  Helmholtz  sought  to  gain  a  greater  re- 
flecting power  and  better  illumination  of  the  fundus,  but  this 
method  is  much  inferior  to  that  which  we  now  use. 

Indirect  Method  of  Ophthalmoscopy. — This  method  of 
examination  consists  in  the  examination  of  the  aerial  image  as 
formed  in  front  of  the  eye.  The  aid  of  a  convex  lens  must  be 
invoked  in  all  conditions  but  the  highest  grades  of  myopia,  since 
otherwise  the  image  if  formed  at  all,  would  be  so  far  in  front 
of  the  eye  that,  although  highly  magnified,  only  a  very   small 


90  Principles    of    Optics 

portion  of  the  fundus  would  be  visible.  The  power  of  the  con- 
vex lens  used  may  be  varied  at  the  convenience  of  the  examiner. 
A  lens  of  13  D,  which  produces  in  emmetropia  a  magnification 
of  about  five  diameters,  is  usually  satisfactory.  When  we  wish 
a  greater  magnification  and  in  myopia  a  weaker  lens  may  be 
used  with  advantage. 

The  lens  should  be  held  so  that  its  focus  lies  in  or  near  the 
plane  of  the  iris  of  the  eye  under  examination.  The  magnifica- 
tion of  the-  pupil  is  then  infinite  or  nearly  so,  the  red  reflex  is 
coextensive  with  the  lens,  and  the  field  of  view  is  correspondingly 
large. 

The  examiner,  looking  through  the  sight  hole  of  the  mirror, 
may  most  easily  see  the  details  of  the  aerial  image  when  he  is 
at  a  distance  of  about  250  mm  from  this  image.  He  may  either 
use  his  accommodation  to  focus  the  rays  diverging  from  the 
image,  or  he  may  make  use  of  a  convex  lens  attached  to  the 
ophthalmoscope  for  this  purpose. 

Direct  Method  of  Ophthalmoscopy. — In  the  direct 
method  the  aim  of  the  ophthalmoscopist  is  to  approach  the  eye 
to  be  examined  as  near  as  is  compatible  with  good  illumination, 
and  to  receive  directly  upon  his  retina  an  inverted  image  of  the 
illuminated  fundus  area.  In  this  method  the  examiner's  eye 
takes  the  place  of  the  convex  lens  used  in  the  indirect  method. . 

In  the  diagram  (Fig.  51)  both  examining  and  examined  eyes 


fig.  51 


are  emmetropic.  All  the  rays  which  emerge  from  any  point  of 
the  illuminated  area  will  be  parallel,  and  some  of  the  rays  from 
the  various  points  of  this  area  will  enter  the  examiner's  eye  and 
will  be  focused  in  an  image  on  his  retina  without  accommodation. 
If  the  examined  eye  is  myopic  the  emergent  rays  will  be 
convergent  (not  yet  having  intersected  in  the  aerial  image)  and 
in  order  that  they  may  be  focused  by  an  emmetropic  examiner 


Ophthalmoscopy,  Skiascopy,  and  Ophthalmometry         91 

without  accommodation  they  must  be  rendered  parallel  by  a  con- 
cave lens. 

If  the  examined  eye  is  hyperopic  the  emergent  rays  will  be 
divergent  and  must  be  rendered  parallel  by  a  convex  lens,  or  by 
exercise  of  the  accommodation. 

//  the  examiner's  eye  is  ametropic  his  error  may  be  corrected 
by  the  proper  lens  of  the  ophthalmoscope  series,  or  he  may  use 
his  ordinary  eyeglasses. 

Since  an  object  is  always  inverted  with  respect  to  the  retinal 
image,  it  is  clear  that  in  this  method  of  examination  the  observer 
will  see  the  fundus  image  in  its  natural  or  erect  position.  This 
image  will  appear  to  be  behind  the  examined  eye.  We  cannot 
assign  any  definite  position  to  the  image.  To  some  persons  it 
may  seem  to  be  quite  near,  while  others  will  project  it  to  a 
greater  distance. 

The  apparent  size  of  the  image  will,  therefore,  vary  accord- 
ing to  the  position  at  which  it  is  supposed  to  be.  The  actual 
magnification  is  due  to  the  fact  that  in  passing  out  of  the 
examined  eye  the  rays  are  rendered  parallel  (or  approximately 
so  if  the  eye  is  ametropic)  and  that  by  this  means  the  examiner 
is  able  to  focus  them  on  his  retina,  and  so  to  see  the  examined 
eye  at  a  very  short  distance.  In  other  words  the  eye  under  exam- 
ination acts  as  a  magnifying  lens  such  as  was  described  in  the 
preceding  chapter. 

If  we  examine  the  diagram  (Fig.  51)  we  see  that  when  both 
eyes  are  emmetropic  the  retinal  image  as  formed  in  the  observer's 
eye  is  of  exactly  the  same  size  as  the  fundus  area  under  exam- 
ination. We  know  that  ordinarily  the  retinal  image  is  much 
smaller  than  the  object  of  vision,  and  we  see  that  in  this  method 
of  examination  the  image  must  be  much  magnified. 

In  estimating  the  magnifying  power  of  microscopes  it  is 
customary  to  compare  the  size  of  the  retinal  image  or  the  visual 
angle  as  it  is  with  that  which  would  be  made  by  the  same  object 
on  the  retina  if  it  were  placed  at  the  ordinary  distance  for  exam- 
ining small  objects.  Because  of  the  limitation  of  our  accommo- 
dative power  we  do  not  usually  examine  an  object  at  a  less 
distance  than  10  inches  or  250  millimeters.  This  distance  is  there- 
fore taken  as  the  standard  of  comparison  in  the  measurement  of 
magnifying  power.  With  this  understanding,  the  magnification 
under  which  the  optic  disk  or  any  other  part  of  the  fundus  is 


92  Principles    of    Optics 

seen  in  direct  ophthalmoscopy  is  about  16  diameters,  for  the 
linear  dimension  of  an  object  placed  256  mm  from  the  nodal  point 
of  the  normal  eye  would  be  16  times  as  great  as  the  corresponding 
dimension  of  its  image  on  the  retina. 

In  hyperopia  the  magnification  is  somewhat  less,  and  it 
diminishes  with  the  increase  of  the  distance  between  the  two  eyes ; 
in  myopia  the  magnification  is  greater  than  in  emmetropia, 
and  it  increases  with  the  distance  between  the  two  eyes. 

Skiascopy. 

In  the  two  preceding  methods  of  examination  it  is  the  pur- 
pose of  the  examiner  to  see  clearly  the  details  of  the  fundus — 
in  the  one  case  by  means  of  an  inverted  aerial  image,  and  in  the 
other  by  focusing  the  emergent  rays  directly  upon  his  own 
retina.  In  the  method  now  to  be  considered  the  object  of  the 
observer  is  not  to  see  distinctly  the  details  of  the  fundus-image, 
but  to  place  his  eye  as  nearly  as  possible  in  the  position  at  which 
the  aerial  image  of  the  examined  eye  would  be  formed,  and  to 
determine  thereby  the  refractive  condition  of  this  eye. 

Point  of  Reversal. — We  have  learned  that  the  myopia  of 
an  eye  is  measured  by  the  distance  at  which  an  object  must  be 
situated  in  order  that  it  shall  be  focused  on  the  retina  without 
accommodation ;  that  is,  by  the  distance  between  the  eye  and  its 
far-point.  Since  the  retina  and  the  far-point  of  an  eye  are 
conjugate,  it  is  apparent  that  the  aerial  image  is  formed  at  the 
far-point,  and  that  the  position  of  this  image  determines  the 
degree  of  myopia. 

Since  the  emergent  rays  coming  from  any  point  of  the 
fundus  intersect  in  the  aerial  image,  their  relative  position  is 
reversed  at  this  point.  The  point  of  reversal  is  therefore  identical 
with  the  far-point  of  the  eye. 

Reversal  of  Movement. — If  by  tilting  the  mirror  the 
illuminated  area  7X  I2  (Fig.  50)  is  shifted  downward  it  is 
apparent  that  the  aerial  image  Ox  02  will  move  upward,  and  if 
the  examiner  is  farther  than  this  image  from  the  examined  eye 
he  may  observe  this  movement,  but  if  he  is  nearer  the  eye  than 
the  point  of  reversal,  the  aerial  image  Ox  0,  will  be  replaced 
by  the  diffusion  image  on  the  examiner's  retina,  as  in  direct 
ophthalmoscopy.  As  the  illuminated  area  7X  I2  moves  downward 
the  diffusion  image  on  the  examiner's  retina  moves  upward,  and 


Ophthalmoscopy,  Skiascopy,  and   Ophthalmometry         93 

consequently  there  is  an  apparent  downward  motion  of  the  illum- 
inated area. 

When  therefore  the  examiner  is  without  the  point  of  reversal 
he  sees  the  light  area  in  the  pupil  move  in  an  opposite  direc- 
tion to  the  actual  movement  of  the  light  area  on  the  fundus  of 
the  eye  under  examination ;  and  when  he  is  within  the  point  of 
reversal  he  sees  the  light  in  the  pupil  move  in  the  same  direc- 
tion as  the  movement  of  the  light  on  the  fundus. 

The  direction  of  the  apparent  movement  of  the  light  area 
is  the  basis  of  skiascopy,  or  the  shadow  test,  which  is  our  most 
reliable  method  for  the  objective  determination  of  the  refractive 
condition  of  an  eye.  In  the  application  of  this  method  the 
examiner's  first  aim  is  to  determine  whether  he  is  within  or 
without  the  point  of  reversal  by  watching  the  movement  of 
the  light  area  in  the  pupil  of  the  examined  eye  while  he 
varies  the  position  of  the  light  on  the  fundus  by  rotating  the 
illuminating  mirror. 

When  he  is  well  within  or  without  the  point  of  reversal 
the  examiner  may  readily  see  the  fundus-image  change  its  posi- 
tion ;  but  when  he  is  near  the  point  of  reversal  he  can  see  no 
details  of  the  fundus,  and  he  must  decide  as  to  the  direction 
of  motion  by  observing  the  variations  of  light  and  shadow  in 
the  pupil. 

Variation  of  Magnification. — In  the  application  of  the 
direct  method  of  ophthalmoscopy  we  may  notice  that  in  examining 
a  myopic  eye  the  magnification  of  the  image  increases  with  an 
increase  of  distance  between  the  two  eyes.  In  ophthalmoscopy 
this  is  not  of  any  practical  importance,  because  we  do  not  to  any 


FIG.    52 

great  extent  change  the  distance  between  the  eyes.  But  in 
skiascopy  in  which  the  distance  between  the  examined  and  the 
examiner's  eye  is  greater,  the  varying  magnification  is  a  funda- 
mental matter.  The  increase  of  magnification  continues  until 
the  examiner's  nodal  point  coincides  with  the  point  of  reversal 


94 


Principles    of    Optics 


of  the  eye  under  examination.  At  this  point  the  magnification  is 
infinite;  or,  to  express  it  in  more  practical  language,  the  single 
point  /  of  the  illuminated  area  will  entirely  fill  the  pupil  P  P  of 
the  eye  under  examination,  as  the  examiner  sees  it.  This  is  easily 
understood    by    an    inspection    of    the    accompanying    diagram 

(Fig.  52). 

We  can  also  understand  from  Fig.  53  that  when  the  ex- 
aminer is  at  Elf  his  retinal  image  of  the  pupil  P  P  coincides, 
not  with  his  image  of  a  single  point  /  as  before,  but  with  his 


fig.  53 

image  of  the  whole  area  Ix  I2.  In  this  case  then  the  magnification 
is  less,  since  a  much  greater  part  of  the  fundus-image  will 
be  seen.  If  he  should  approach  still  nearer  the  eye  without 
enlarging  the  area  of  illumination  on  the  examined  eye,  this  area 
would  no  longer  fill  the  entire  pupil,  which  would  therefore 
appear  as  a  dark  ring  surrounding  a  bright  center.  Practically, 
however,  as  we  get  nearer  the  eye  the  area  of  illumination  is 
increased,  so  that  the  entire  pupil  is  ordinarily  illuminated. 

When  the  examiner  is  without  the  point  of  reversal,  the 
magnification  (which  is  now  negative)  diminishes,  and  if  he  is 
at  E2  (Fig.  54)  his  retinal  image  of  Ox  02,  corresponding  to  the 


area  Ix  I2,  coincides  with  his  image  of  the  pupil  P  P,  just  as  it  did 
when  he  was  at  Ex. 

Movement  of  the  Shadow  Line. — Let  us  again  suppose 
the  examiner's  eye  to  be  at  E2  and  Ix  I2  to  be  the  illuminated 
area  of  the  fundus.  Under  these  conditions  the  entire  pupil  P  P 
glows  with  the  red  reflex.    If  now  the  light  area  is  shifted  down- 


Ophthalmoscopy,  Skiascopy,  and   Ophthalmometry         95 

ward  by  rotation  of  the  mirror,  so  that  the  upper  half  /  7X  is  no 
longer  illuminated,  the  corresponding  part  0  Ox  of  the  aerial 
image  will  be  unilluminated — that  is,  the  lower  part  of  the 
pupillary  space  will  appear  in  shadow. 

As  the  area  of  illumination  continues  to  move  downward 
the  shadow  moves  upward,  and  when  the  light  has  been  shifted 
so  far  downward  as  to  leave  the  entire  area  Ix  I2  in  darkness,  the 
image  will  have  moved  so  far  upward  as  to  have  passed  out  of 
the  examiner's  range  of  vision ;  that  is,  it  will  be  above  the  pupil 
of  the  examined  eye,  and  the  latter  will  appear  to  the  examiner 
to  be  in  darkness. 

The  rapidity  with  which  the  shadow  moves  across  the  pupil 
varies  with  the  examiner's  position  with  reference  to  the  point 
of  reversal,  being  the  more  rapid  as  he  approaches  this  point. 
When  he  is  at  this  point  the  entire  pupil  glows  as  long  as  the  single 
point  /  is  illuminated,  and  when  the  light  passes  below  /  dark- 
ness quickly  covers  the  pupil.  When  he  is  near,  but  not  at  the 
point  of  reversal,  the  examiner  sees  the  shadow  move  very 
rapidly  across  the  pupil  as  the  light  area  is  shifted  by  rotating 
the  mirror. 

When  the  examiner  passes  within  the  point  of  reversal  (as  at 
£a)  the  shadow  again  begins  to  move  more  slowly,  but  now,  as  the 
light  area  moves  downward,  the  upper  portion  of  the  pupil 
appears  to  be  in  shadow,  and  the  border  line  between  light  and 
shade  moves  downward.  It  now  moves  in  the  same  direction 
as  the  light  area  on  the  fundus  of  the  eye  undergoing 
examination. 

In  emmetropia  and  in  hyperopia  the  examiner  is  always 
within  the  point  of  reversal.  It  is  necessary,  therefore,  in  the 
practical  application  of  the  shadow  test  to  place  a  convex  lens 
before  the  examined  eye  to  bring  the  point  of  reversal  to  a  con- 
venient position. 

Is  the  point  of  reversal  governed  by  the  position  of  the  nodal 
point  or  of  the  pupil  of  the  examiner's  eye?  In  answer  to  this 
question  we  may  say  that  practically  it  makes  no  difference  which 
of  the  two  we  regard  as  the  critical  point.  Since  the  nodal  point 
and  the  pupil  are  in  such  close  proximity  as  compared  with  the 
distance  between  the  two  eyes,  it  is  of  no  importance  whether 
we  measure  from  the  nodal  point  or  from  the  pupil.  From  a 
theoretical  point  of  view,  however,  the  answer  is  not  so  easy. 


96  Principles    of    Optics 

In  the  explanation  of  the  principles  of  this  method  of  exam- 
ination some  European  authors  have  maintained  with  plausible 
reasoning  that  the  examiner's  eye  is  at  the  point  of  reversal 
when  his  pupil  (not  the  nodal  point)  is  situated  at  the  far  point 
of  the  examined  eye.  For  an  explanation  of  this  point  of  view 
let  us  refer  to  Fig.  52.  Suppose  that  the  light  moves  from  / 
towards  I2.  As  it  so  moves  the  conjugate  O  moves  upward,  and 
the  upper  rays  are  cut  off  by  the  upper  border  of  the  pupil  sooner 
than  the  lower  rays.  There  will,  therefore,  be  an  apparent 
motion  in  the  same  direction  as  the  light  area,  although  the  ex- 
aminer's nodal  point  is  at  the  point  of  reversal.  If  now  he 
moves  farther  from  the  eye  so  that  the  conjugate  O  falls  in  the 
pupillary  plane,  all  the  rays  will  be  intercepted  at  once,  and  be- 
yond this  point  the  rays  will  be  reversed. 

But  if  we  accept  this  reasoning,  which  appears  to  be  sound, 
we  are  confronted  with  another  difficulty;  namely,  that  it  is  only 
when  the  examiner's  nodal  point  is  at  the  conjugate  O  that  the 
single  point  of  light  /  fills  the  entire  pupil  P  P.  It  is  possible, 
therefore,  that  in  the  strictest  sense  there  may  be  no  absolute 
point  of  reversal.* 

Form  of  the  Shadow  Line. — The  light  area  on  the  retina 
will  be  circular,  or  approximately  so,  since  the  light  is  reflected 
by  a  circular  mirror  and  enters  the  eye  through  a  circular 
aperture,  the  pupil.  The  shadow  edge  must,  therefore,  corres- 
pond more  or  less  closely  to  the  arc  of  a  circle.  The  curvature 
of  this  arc  will  vary  with  the  portion  of  the  outline  of  the  light 
area  which  falls  within  the  range  of  vision ;  that  is,  the  edge 
will  be  more  curved  as  the  magnification  is  less,  or  according 
as  the  examiner  is  at  a  greater  distance  from  the  point  of  re- 
versal. When  he  is  near  this  point  the  border  line  of  the  shadow 
appears  only  slightly  if  at  all  curved. 

Illumination  of  the  Retina. — If  a  plane  mirror  is  used 
to  illuminate  the  retina,  the  apparent  source  of  light  is  behind 
the  mirror ;  but  when  the  concave  mirror  is  used  an  aerial  image 
of  the  flame  will  be  formed  in  front  of  the  mirror,  and  this  will 
be  the  apparent  source  of  illumination.  We  readily  see  that 
with  the  plane  mirror  the  motion  of  the  apparent  source  of  illum- 


*This  is  upon  the  assumption  that  the  illumination  of  the  fundus  is  confined  to 
a  single  point,  which  is  never  the  case;  it  is  apparent  therefore  that  on  this  account 
and  also  because  of  spherical  aberration  there  cannot  be  a  single  point  of  reversal 
for  all  the  emergent  rays. 


Ophthalmoscopy,  Skiascopy,  and   Ophthalmometry         97 

ination  is  opposite  to  the  direction  of  rotation  of  the  mirror, 
while  with  the  concave  mirror  the  apparent  source  of  illumination 
moves  in  the  same  direction  as  the  rotation  of  the  mirror.  It  is 
also  evident  that  the  motion  of  the  light  area  on  the  retina  is 
opposite  in  direction  to  the  motion  of  the  apparent  source  of 
illumination.  Therefore  with  the  plane  mirror  the  light  area  on 
the  retina  moves  in  the  same  direction  as  the  tilting  of  the  mirror, 
while  with  the  concave  mirror  the  light  area  moves  in  the  opposite 
direction  to  the  tilting  of  the  mirror. 

We  have  so  far  regarded  the  illuminated  area  Ix  I2  as  the 
same  in  the  various  positions  of  the  examiner;  but  in  reality 
when  he  changes  his  position  he  also  changes  the  position  of  the 
mirror  and  with  it  the  apparent  point  of  origin  of  the  illuminat- 
ing rays.  We  have  learned  that  with  the  same  source  of  illum- 
ination the  light  area  on  the  fundus  is  more  diffused  according 
as  the  point  of  origin  of  the  rays  is  more  remote  from  the  point 
of  reversal.  Therefore,  in  order  that  we  may  have  a  bright, 
well  focused  light  area,  giving  a  sharp  contrast  between  light 
and  shade,  we  should  so  arrange  the  light  that  as  the  examiner 
approaches  the  point  of  reversal  the  apparent  source  of  illum- 
ination should  also  be  near  this  point.  This  may  be  most  con- 
veniently accomplished  by  having  a  small  electric  lamp  attached  to 
a  plane  mirror,  so  that  the  apparent  source  of  illumination  is  a 
short  distance  behind  the  mirror. 

Two  Points  of  Reversal  in  Astigmia. — In  regular 
astigmia  there  is  a  separate  point  of  reversal  for  each  principal 
meridian,  and  when  the  examiner  is  at  this  point  for  one  meri- 
dian he  will  be  remote  from  that  for  the  other  principal  meridian, 
the  more  so  according  as  the  astigmia  is  greater.  The  rate  of 
the  shadow  movement  will  therefore  be  different  in  the  two 
principal  meridians.  If  this  movement  is  such  as  to  indicate 
that  the  examiner  is  at  the  point  of  reversal  in  one  meridian 
there  will  be  a  well  denned  shadow  motion  in  the  other  meridian, 
and  this  will  be  with  or  against  the  motion  of  the  light  area 
according  as  in  the  second  meridian  there  is  less  or  more  refrac- 
tion than  in  the  first  meridian. 

Rectilinear  Shadow  Lines  in  Astigmia. — The  appear- 
ance of  a  band  of  light  bordered  by  a  straight  shadow  edge  is 
indicative  of  astigmia.  This  effect  is  produced  when  the  ex- 
aminer is  at  or  near  the  point   of   reversal   for   one  principal 


98  Principles    of    Optics 

meridian.  When  he  is  at  this  point  the  magnification  is  infinite 
as  regards  this  meridian,  but  it  is  less  in  the  other  meridian. 
Therefore  the  circular  or  oval  light  area  will  be  so  magnified 
in  the  first  meridian  without  a  corresponding  magnification  in 
the  second  meridian  that  it  will  appear  in  the  pupil  as  a  band 
of  light  extending  entirely  across  the  pupil  in  the  more  mag- 
nified meridian.  Since  the  magnification  is  infinite  in  this  direc- 
tion, the  lines  which  separate  the  light  from  shade  must  appear  as 
straight  lines. 

The  band  of  light  is  most  distinctly  seen  when  the  apparent 
source  of  illumination  is  conjugate  to  the  fundus  in  the  meridian 
in  which  the  shadow  appears.  With  the  plane  mirror  this 
arrangement  is  effected  when  the  observer  is  at  the  point  of 
reversal  nearer  to  the  eye  while  the  image  of  the  flame  is  at  the 
mo&re  remote  point  of  reversal  (Jackson). 

Summary  of  Underlying  Principles  of  Skiascopy. — 
The  practical  application  of  the  shadow  test,  which  will  be  con- 
sidered in  a  subsequent  chapter,  does  not  ordinarily  present  any 
great  difficulty ;  but  the  optical  principles  involved,  which  I  have 
endeavored  to  explain,  require  very  careful  study  that  they  may 
be.  properly  understood.  The  following  summary  gives  the  more 
important  points  to  be  borne  in  mind. 

( i )  .  The  point  of  reversal  corresponds  to  the  far  point 
of  the  eye,  either  alone  or  in  combination  with  a  lens.  If  the  eye 
is  not  myopic  a  convex  lens  must  be  placed  before  it  so  as  to 
bring  the  point  of  reversal  to  a  convenient  position. 

(2)  When  the  examiner  is  within  the  point  of  reversal  the 
shadow  line  moves  in  the  same  direction  as  the  tilting  of  the 
mirror  if  this  is  plane,  and  it  moves  in  the  opposite  direction  if 
the  mirror  is  concave. 

(3)  When  the  examiner  is  without  the  point  of  reversal  the 
shadow  line  moves  in  the  opposite  direction  to  the  tilting  of  a 
plane  mirror,  and  in  the  same  direction  as  the  tilting  of  a  concave 
mirror. 

(4)  When  the  examiner  is  remote  from  the  point  of  reversal 
the  movement  is  slow  and  the  shadow  is  dense ;  when  he 
is  near  the  point  of  reversal  the  movement  is  rapid  and  the 
shadow  is  faint. 

(5)  A  bright  band  of  light  bordered  by  a  straight  shadow 
edge  is  characteristic  of  astigmia. 


Ophthalmoscopy,  Skiascopy,  and  Ophthalmometry         99 

Ophthalmometry 

Although  the  word  ophthalmometry — measurement  of  the 
eye — is  etymologically  coextensive  with  optometry,  its  use  is  re- 
stricted by  custom  to  the  actual  measurement  of  the  curvature  of 
the  refracting  surfaces. 

When  rays  of  light  impinge  upon  the  cornea,  they  for  the 
most  part  penetrate  this  substance,  but,  as  we  have  learned,  some 
of  the  light  is  reflected ;  the  surface  of  the  cornea  acts  as  a  con- 
vex mirror,  and  a  small,  erect,  virtual  image  of  the  illuminating 
object  is  formed  by  the  reflection  (Fig.  55).  Similarly,  when 
the  light  reaches  the  posterior   surface  of  the  cornea  a  small 


fig.  55 

The  Images  of  Purkinje   (Tscherning) 

The  corneal  images  in  the  middle;  the  images  of  the  anterior  surface  of  the 
crystalline  lens  on  the  right;  those  of  the  posterior  surface  of  the  crystalline  lens 
on  _  left.  The  images  reflected  from  the  posterior  surface  of  the  cornea  are  not 
visible. 

portion  is  turned  back  by  reflection.  Owing  to  the  fact  that  the 
difference  of  refractive  index  between  the  cornea  and  the 
aqueous  humor  is  slight  very  little  light  is  reflected  at  the 
posterior  surface  of  the  cornea,  and  the  image  is  correspond- 
ingly faint. 

At  the  anterior  surface  of  the  crystalline  lens  still  another 
reflection  occurs,  and  again  we  have  a  virtual  image  produced 
by  the  reflection  at  the  convex  surface  of  the  lens.  Finally 
a  real  inverted  image  of  the  illuminating  object  is  formed  by 
reflection  from  the  posterior  surface  of  the  lens,  which  acts  as  a 
concave  mirror. 


ioo  Principles   of    Optics 

The  ophthalmometer  is  a  contrivance  for  measuring  the 
curvature  of  the  refracting  surfaces  of  the  eye  by  means  of  the 
images  of  Purkinje,  which  have  just  been  described. 

In  order  that  we  may  make  use  of  the  reflected  images  for 
measuring  the  curvature  of  the  surfaces  we  must  examine  the 
images  through  a  magnifying  apparatus.  This  apparatus  is 
called  the  telescope  of  the  ophthalmometer,  although  it  does  not 
conform  to  the  technical  definition  of  a  telescope.* 

The  first  attempt  to  measure  the  curvature  of  the  anterior 
surface  of  the  cornea  by  means  of  the  reflected  image  was  made 
by  Home  and  Ramsden  (1795)  in  their  endeavor  to  ascertain 
whether  there  was  an  increase  of  curvature  of  the  cornea  in 
accommodation.  They  used  for  this  purpose  a  microscope  of  low 
power,  in  the  eyepiece  of  which  they  placed  a  micrometer  scale  for 
the  measurement  of  the  image.  Later  Kohlrausch  (1839)  under- 
took to  measure  the  radius  of  the  cornea  in  a  number  of  eyes, 
using  the  same  method.  The  results  were  not  satisfactory,  how- 
ever, since  it  is  impossibe  for  an  eye  to  remain  immovable  during 
the  process  of  measurement. 

Helmholtz,  therefore,  who  devised  the  first  successful 
ophthalmometer  (1854),  used,  in  measuring  the  radius  of  the 
anterior  surface  of  the  cornea,  the  method  of  doubling  the  image 
— a  method  which  has  long  been  used  in  astronomical  work. 

By  looking  through  a  double  prism  (with  one  eye  excluded) 
at  a  drawing  such  as  A  B  (Fig.  56)  one  can  easily  understand 


fig.  56 

how  the  principle  of  doubling  the  image  is  applied  in  ophthal- 
mometry. When  the  prism  is  properly  placed  before  the  eye 
two  images  of  A  B  appear.  The  amount  of  separation  between 
the  two  images  varies  with  the  distance  of  the  prism  from  the 


*A  telescope  is  an  optical  instrument  so  constructed  that  the  parallel  entering 
rays  are  also  parallel  when  they  emerge  from  the  apparatus.  _  It  is  therefore  a 
contrivance  for  examining  distant  objects,  while  a  magnifying  apparatus  for 
examining    near    objects    is   called   a    microscope. 


Ophthalmoscopy,   Skiascopy,   and   Ophthalmometry       101 

line  A  B,  and  by  suitable  adjustment  of  this  distance  the  observer 
may  bring  the  double  images  into  contact,  as  is  shown  in  Fig.  57. 
It  is  apparent  that  in  this  condition  the  amount  of  displacement 
produced  by  the  prism  is  exactly  equal  to  the  length  of  A  B. 
If  therefore  we  know  the  strength  of  the  prism  and  the  posi- 
tion at  which  the  contact  image  is  formed,  we  can  determine  the 
distance  between  A  and  B.    If,  for  instance,  we  are  using  a  one 


B 


fig.  57 

diopter  prism  (each  of  the  component  prisms  having  one-half 
of  this  power),  and  the  contact  position  occurs  at  a  distance  of 
one  meter,  we  know  that  the  length  of  A  B  is  T^  of  a  meter, 
as  follows  from  the  definition  of  a  prism  diopter.  If  the  con- 
tact position  should  occur  at  a  distance  of  two  meters,  the  length 
of  the  line  A  B  would  be  Tfo  of  a  meter  (2  cm),  and  so  on 
for  other  distances  of  the  contact  position. 

When  we  use  a  doubling  device  in  ophthalmometry  we  copy 
the  foregoing  procedure.  The  ophthalmometer  is  provided  with 
two  small  luminous  objects,  called  mires,  the  reflected  images  of 
which  we  examine  in  the  telescope  of  the  ophthalmometer,  and 
by  the  proper  manipulation  of  the  instrument  we  get  the  contact 
position  as  shown  in  Fig.  57. 

Helmholtz  obtained  the  double  images  in  his  ophthalmometer 
by  means  of  two  plates  of  glass  inclined  at  an  angle  which 
could  be  varied  by  the  operator.*  Thus  instead  of  changing  the 
position  of  the  prism,  as  in  our  illustration,  he  changed  the 
doubling  power  of  the  plates  by  varying  their   inclination. 

*Two  plates  of  glass  inclined  at  an  oblique  angle  produce  double  images  by 
means  of  the  lateral  displacement  which  the  rays  undergo  on  account  of  the 
thickness   of  the   glass. 


102 


Principles   of    Optics 


Helmholtz's  apparatus  served  a  very  useful  purpose,  but 
because  of  the  great  distance  (about  six  feet)  between  the  ex- 
aminer and  the  eye  under  examination,  and  because  there  was  no 
ready  means  of  finding  the  meridians  of  greatest  and  least 
refraction,  this  ophthalmometer  was  suitable  only  for  laboratory 
investigations,  and  not  for  the  measurement  of  corneal  asymmetry 
— the  purpose  for  which  modern  ophthalmometers  are  designed. 

The  means  by  which  J  aval  and  Schidtz  (1882)  made  ophthal- 
mometry a  practical  method  for  the  ready  determination  of 
corneal  asymmetry  consisted  in  the  shortening  of  the  focal  length 
of  the  telescope;  in  the  adoption  of  mires  which  quickly 
reveal  the  meridians  of  greatest  and  least  refraction;  and  in 
having  the  various  parts  so  proportioned  and  arranged  that  the 
amount  of  astigmia  in  diopters  is  shown  to  the  examiner 
without  any  preliminary  calculation. 

In  the  Javal-Schiotz  ophthalmometer  the  doubling  is  pro- 
duced by  the  Wollaston  prism  of  quartz — a  substance  which  has 
the  property  of  polarizing  light  and  producing  double  refraction. 

The  Wollaston  prism  consists  of  two  prisms  of  quartz  prop- 
erly cut  with  reference  to  the  polarizing  axes  and  cemented 
together   (Fig.  58).     Each  ray  which  passes  through  the  prism 


Wollaston    Prism 
FIG.    58 

is  divided  into  two  rays,  as  shown  in  the  illustration,  so  that  an 
object  seen  through  the  prism  appears  double. 

The  telescope  of  this  ophthalmometer  consists  of  an  eye- 
piece and  a  double  objective,  the  birefringent  prism  being  placed 
between  the  two  lenses  of  the  objective.  Since  this  prism 
occupies  a  fixed  position  its  doubling  power  cannot  be  varied.  The 
contact  position  of  the  double  images  must  therefore  be  gotten 


Ophthalmoscopy,   Skiascopy,   and    Ophthalmometry        103 

by  making  the  size  of  the  image  conform  to  the  fixed  doubling 
power  of  the  prism. 

Each  lens  of  the  objective  has  a  focal  length  of  270  mm. 
The  image  under  examination  is  at  the  principal  focus  of  the 
first  lens.  Rays  reflected  from  any  point  of  the  cornea  will  be 
parallel  after  passing  through  this  lens.  They  then  enter  the 
Wollaston  doubly  refracting  prism,  and  are  divided  into  two  sets 
(each  of  which  gives  an  image)  ;  they  are  then  further  re- 
fracted by  the  second  lens  of  the  objective,  and  are  focused 
at  a  distance  of  270  mm  from  the  lens;  for  the  rays,  having 
been  rendered  parallel  by  the  first  lens,  must  now  be  focused 
at  the  principal  focus  of  the  second  lens.  Since  the  objective  as 
a  whole  thus  occupies  the  midway  position  between  the  two 
conjugate  foci,  we  see  that  the  image  as  formed  at  the  focus  of 
the  eyepiece  must  have  the  same  size  as  the  image  formed  by 
reflection  at  the  cornea.  But  the  image  at  the  eyepiece  has 
been  doubled  by  the  prism,  and  if  the  separation  between  these 
two  images  can  be  made  equal  to  the  diameter  of  the  image,  the 
two  images  will  be  seen  in  the  contact  position.  The  prism, 
as  used  in  this  instrument,  causes  a  separation  of  about  3  mm, 
and  by  altering  the  distance  between  the  mires  we  can  make 
this  distance  such  that  the  image  as  reflected  from  the  cornea 
exactly  equals  the  amount  of  separation,  and  the  two  images 
will  then  be  seen  in  the  contact  position. 

When  we  have  by  this  means  determined  the  size  of  the 
corneal  image,  we  can  deduce  the  radius  of  curvature  of  the 
cornea  which  corresponds  to  this  image.  By  determining  this 
curvature  in  the  two  principal  meridians  we  find  the  amount  of 
astigmia  which  results  from  any  existing  corneal  asymmetry. 

The  method  adopted  by  Javal  and  Schiotz  for  marking  the 
principal  meridians  and  measuring  the  asymmetry  is  shown  in 


fig.  59 


Fig-  59-  One  of  the  mires  is  a  rectangle  and  the  other  consists 
of  a  series  of  rectangular  steps.  A  straight  black  line  runs 
through  the  middle  of  each  mire. 


104 


Principles   of    Optics 


When  the  plane  of  deviation  of  the  prism  corresponds  with 
either  one  of  the  principal  meridians  the  two  images  retain  their 
rectangular  form  and  the  line  running  through  one  mire 
forms  a  continuation  of  that  running  through  the  middle  of 
the  other.  But  in  any  oblique  meridian  the  rectangles  are 
distorted  so  as  to  appear  as  oblique  parallelograms,  and  the 
middle  lines  are  not  continuous  with  each  other.  This  phe- 
nomenon of  toric  reflection  is  analogous  to  what  we  learned  in 
studying  toric  refraction.  As  we  then  saw  that  rays  meeting 
the  toric  surface  in  an  oblique  meridian  would  not  lie  in  a  com- 
mon meridian  after  refraction,  so  it  is  with  the  reflected  rays. 
The  reflected  images  of  the  two  mires  will  not  lie  in  a  common 


:<    d 

FIG.    60 

Explanation   of  the  Difference  in   Level    (7 'scheming) 


meridian;  one  of  the  images  will  be  higher  or  lower  than  the 
othef.    This  is  illustrated  in  Fig.  60. 

If  the  cornea  is  symmetrical,  the  images  appear  as  in  the 
dotted  outline;  that  is,  in  any  meridian  in  which  the  mires  may 


Ophthalmoscopy,   Skiascopy,   and   Ophthalmometry        105 

be  placed,  their  outside  double  images  are  always  tangent  to  the 
circle  of  the  dotted  outline.  But  when  the  cornea  is  asymmetric 
the  images  are  smaller  in  the  meridian  of  greatest  curvature  than 
in  that  of  least  curvature,  and  as  the  mires  are  revolved  from 
one  principal  meridian  to  the  other  the  outside  images  (H  and 
G)  describe  an  ellipse  as  in  the  diagram,  and  since  the  doubling 
takes  place  in  the  plane  of  the  prism,  the  middle  lines  of  the 
two  inside  images  (K  and  L)  do  not  now  lie  on  the  diameter  of 
the  circle,  but  lie  on  opposite  sides  of  this  diameter.  The  princi- 
pal meridians  are  therefore  marked  by  the  two  directions  in 
which  the  lines  passing  through  the  middle  of  the  mires  appear 
to  be  a  continuous  line. 

The  series  of  steps,  as  used  in  one  of  the  mires,  was  devised 
for  the  ready  measurement  of  astigmia.  The  image  which  cor- 
responds to  each  step  is  regarded  as  representing  one  diopter  of 
refraction.  This  is  only  approximately  true,  since  the  proportion 
of  the  mire  which  corresponds  to  one  diopter  varies  with  the 
radius  of  curvature.  Each  step  corresponds  to  one  diopter  when 
the  reflected  image  is  2.94  mm  in  diameter.  When,  therefore, 
there  is  an  overlapping  of  several  steps  the  image  is  less  than 
2.94  mm,  and  the  steps  do  not  accurately  measure  the  number  of 
diopters  of  astigmia.  In  the  lower  degrees  of  asymmetry  we 
may  rely  upon  the  overlapping  of  the  steps,  but  in  the  higher 
degrees  we  obtain  a  more  accurate  result  by  reading  from  the 
scale  attached  to  the  instrument. 

With  the  addition  of  modern  mechanical  adjustments  the 
Javal-Schiotz  ophthalmometer  surpasses  all  other  instruments  of 
this  kind  in  the  accuracy  of  its  measurements. 

An  extended  experience  with  the  various  devices  for  doubling  the 
image  has  convinced  me  that  the  Wollaston  prism  alone  of  the  available 
means  can  be  relied  upon  to  give  a  sufficiently  accurate  result  for  the 
measurement  of  small  degrees  of  corneal  astigmia. 

I  base  this  opinion  upon  the  results  of  my  own  practice  with  the 
artificial  cornea  as  well  as  upon  the  results  which  I  have  seen  in  the 
attempts  of  several  skilled  manipulators  to  mark  the  contact  position  in 
repeated  measurements  by  a  uniform  position  of  the  pointer  on  the 
recording  scale. 

The  inaccuracy  which  results  from  the  use  of  the  glass  doubling 
devices  is  due  chiefly  to  the  fact  that  when  they  are  used  the  depth  of 
focus  is  greater  than  with  the  quartz  prism.  When  the  latter  is  used  the 
slightest  error  of  adjustment  produces  a  blurred  image;  whereas,  with  the 
former  the  adjustment  of  the  instrument  (or  the  position  of  the  eye  under 
examination)  may  be  so  varied  as  to  affect  very  materially  the  doubling 
action  of  the  prism  without  marring  the  sharpness   of  the   image.     An 


106  Principles    of    Optics 

error  of  .50  D  or  more  may  readily  be  made  from  this  cause  by  a  careful 
observer. 

Javal  and  Schiotz  placed  the  prism  of  their  instrument  be- 
tween the  two  lenses  of  the  objective  in  order  that  the  rays  from 
any  point  of  the  image  would  be  parallel  in  passing  through  the 
prism,  for,  as  we  have  learned,  parallel  rays  do  not  undergo  the 
relative  distortion  to  which  divergent  or  convergent  rays  are 
subject  in  traversing  a  prism. 

A  double  prism  of  glass  affords  a  greater  intensity  of  illum- 
ination than  does  the  quartz  prism.  With  the  former  we  may 
use  a  small  aperture  and  obtain  clear  images  by  placing  the  prism 
between  the  objective  and  the  eyepiece.  With  this  arrangement 
the  mires  may  remain  stationary  while  the  contact  position  is 
obtained  by  moving  the  prism  in  the  tube  of  the  telescope,  as  in 
the  Chamber s-Inskeep  ophthalmometer. 

Of  other  appliances  for  measuring  the  curvature  of  the 
anterior  surface  of  the  cornea  only  the  keratometer  of  Sut cliff e 
requires  especial  mention.  The  unique  feature  of  this  instrument 
is  that  the  curvature  is  measured  simultaneously  in  the  two 
principal  meridians  of  the  cornea.  There  are  two  pairs  of  mires 
and  each  pair  is  doubled  in  its  own  meridian.  The  doubling  is 
accomplished  by  means  of  movable  cylindrical  lenses  of  weak 
power  which  are  placed  between  the  two  lenses  of  the  objec- 
tive. As  these  cylinders  are  moved  transversely  they  present 
varying  degrees  of  prismatic  action. 

Keratometry  and  Phakometry. — Helmholtz  designed 
his  ophthalmometer  not  only  for  measuring  the  anterior  surface 
of  the  cornea,  but  for  measuring  also,  though  by  a  more  compli- 
cated process,  the  two  surfaces  of  the  crystalline  lens.  Javal 
and  Schiotz,  on  the  other  hand,  intended  their  instrument  solely 
for  measuring  the  curvature  of  the  anterior  surface  of  the 
cornea.  It  is  not,  therefore,  in  the  fullest  sense,  an  ophthal- 
mometer, for  ophthalmometry  includes  both  keratometry 
(measurement  of  the  cornea)  and  phakometry  (measurement  of 
the  lens).  So  also  other  modern  ophthalmometers  are  designed 
for  measuring  corneal  astigmia  only,  and  they  are  sometimes 
called  kcratometcrs. 

From  a  practical  standpoint  keratometry  is  more  import- 
ant than  phakometry,  for  the  main  cause  of  the  higher  degrees 


Ophthalmoscopy,   Skiascopy,    and    Ophthalmometry        107 

of  astigmia  is  found  in  asymmetry  of  the  anterior  surface  of 
Che  cornea.  But  phakometry  also  has  its  usefulness,  for  in  the 
lower  degrees  of  astigmia  no  reliable  information  is  furnished 
by  keratometry  except  in  conjunction  with  phakometry. 

With  his  ophthalmo-phakometcr  Tscherning  has  been 
enabled  to  measure  the  curvature  of  the  posterior  surface  of  the 
cornea  and  of  the  two  surfaces  of  the  crystalline  lens.  But  as 
several  difficult  observations  must  be  made,  and  the  curvature 
deduced  from  trigonometrical  calculation,  this  method  is  suitable 
only  for  laboratory  investigations. 

I  have  had  an  ophthalmometer  constructed  with  which  I  can 
apply  the  method  of  doubling  to  the  direct  measurement  of  the 
two  surfaces  of  the  crystalline  lens.  The  basis  of  this  apparatus 
is  the  Javal-Schidtz  ophthalmometer.  But  in  order  that  this  may 
be  adapted  for  measuring  the  two  surfaces  of  the  lens  as  well 
as  the  anterior  surface  of  the  cornea,  two  radical  changes  in  con- 
struction are  required. 

The  first  of  these  innovations  is  in  the  mires,  in  order  that 
sufficient  illumination  may  be  secured  for  the  lens  measurements. 
The  opalescent  glass  is  made  readily  removable  by  means  of  a 
rotating  disk,  so  that  in  measuring  the  lens  the  unshaded  fila- 
ments of  two  small  electric  lamps  are  used  as  mires. 

The  second  innovation  is  required  in  order  to  adapt  the  in- 
strument to  the  great  variation  in  the  size  of  the  images  as 
formed  at  the  posterior  surface  of  the  lens  and  at  the  anterior 
surface  with  magnification  by  the  cornea.  We  must  provide 
for  a  variation  in  radius  of  curvature  from  5  mm,  for  the 
posterior  surface  of  the  lens,  to  20  mm,  which  represents  the 
apparent  radius  when  the  actual  radius  of  the  anterior  surface 
is  12  mm. 

The  adaptation  of  the  instrument  to  this  great  variation  of 
curvature  is  accomplished  by  making  the  objective  and  the 
prism  movable  in  the  tube  of  the  telescope.  By  varying  in  this 
way  the  relative  size  of  the  image  at  the  eyepiece  as  compared 
with  the  actual  image  under  measurement,  the  images  formed 
at  all  three  surfaces  can  be  measured.  The  required  movement 
of  the  objective  is  not  so  great  as  to  mar  the  sharpness  of 
the  images  because  of  divergency  or  convergency  of  the  rays 
as  they  traverse  the  prism. 


io8  Principles   of    Optics. 

The  images  formed  at  the  anterior  surface  of  the  lens  are 
diffuse  and  indistinct,  and  a  slight  movement  of  the  eye  throws 
them  out  of  view.  It  is  therefore  not  easy  to  measure  the  curva- 
ture of  this  surface ;  in  fact  it  is  not  possible  without  intelligent 
co-operation  on  the  part  of  the  examinee.  Furthermore  we  cannot 
determine  with  exactness  the  real  from  the  magnified  image 
unless  we  know  the  position  of  the  surface,  which  is  not  deter- 
mined in  this  method.  The  measurement  of  the  anterior  surface 
is  therefore  an  approximation,  which  is  based  upon  an  average 
curvature  of  the  cornea  and  an  average  depth  of  the  anterior 
chamber;  but  as  we  need  know  only  the  difference  in  curvature 
in  the  two  principal  meridians  for  the  determination  of  astigmia, 
and  as  a  decided  difference  of  curvature  causes  only  a  slight 
degree  of  astigmia  at  this  surface,  the  accuracy  attainable  is 
sufficient  for  practical  purposes.  In  fact,  as  I  shall  show  in  the 
further  consideration  of  this  subject  in  the  appendix,  the  anterior 
surface  of  the  lens  is  a  subordinate  factor  in  the  production  of 
astigmia. 

The  posterior  surface  of  the  lens  is  so  situated  with  refer- 
ence to  the  refractive  properties  of  the  eye  that  the  reflected 
images  are  not  altered  in  size  by  refraction.  These  images  are 
distinct,  and  we  can  therefore  measure  the  posterior  surface 
with  accuracy. 

Determination  of  Astigmia  by  Ophthalmometry. — 
By  means  of  the  measurement  of  the  curvature  of  the  cornea  or 
lens,  we  may  determine  the  astigmia  which  results  from  asymmetry 
of  any  of  these  surfaces.  We  do  this  by  expressing  the  recip- 
rocal of  the  anterior  focal  length  as  the  dioptric  equivalent  in 
each  of  the  meridians  measured,  and  by  taking  the  difference 
between  the  dioptric  equivalent  in  the  two  principal  meridians. 
This  difference  represents  the  dioptric  power  of  the  correcting 
lens  as  applied  directly  to  the  surface  under  measurement.  We 
ordinarily  neglect  the  error  which  we  incur  from  the  fact  that 
the  correcting  lens  cannot  be  placed  in  contact  with  the 
cornea,  although  this  error  is  at  times  very  considerable. 

The  method  of  determining  the  astigmia  from  the  ophthal- 
mometric  observations  will  be  more  fully  explained  in  the 
appendix.  It  suffices  to  say  here  that  in  estimating  the  focal  length 
of  the  cornea  we  do  not  assign  the  index  of  the  cornea,  but  that 
of  the  aqueous  humor.     If,  as  is  probable,  the  posterior  surface 


Ophthalmoscopy,   Skiascopy,   and    Ophthalmometry        109 

of  the  cornea  follows  the  asymmetry  of  the  anterior  surface, 
we  incur  no  appreciable  error  by  doing  this  and  neglecting  the 
posterior  corneal  refraction.  T scheming  thinks,  however,  that  the 
curvature  of  the  posterior  surface  of  the  cornea  is  almost  in- 
variably greater  in  the  vertical  than  in  the  horizontal  meridian. 
If  this  is  true  an  error  in  the  measurement  of  corneal  astigmia 
results  when  the  curvature  of  the  anterior  surface  of  the  cornea 
is  greatest  in  the  horizontal  meridian. 

The  following  authorities  have  been  consulted  in  the  prep- 
aration of  the  foregoing  chapter: 

Helmholtz,   Optique  Physiologique,  and   Ueber  die  Accom- 
modation des  Auges,  Arch,  fiir  Ophth.,  1855. 

Briicke,  Ueber  das  Leuchten  der  Menschl.  Augen,  Mueller's 
Arch,  fiir  Anat.  und  Phys.,  1847. 

Gould,  The  Ophthalmoscope  and  the  Art  of  Ophthalmoscopy, 
in  Norris  and  Oliver's  System  of  Diseases  of  the  Eye. 

Landolt,  Refraction  and  Accommodation  of  the  Eye;  and 
Die  Untersuchungensmethoden,  Graefe-Saemisch,  2d  ed. 

Jackson,  Skiascopy. 

Ruppell,   Zur   Skiascopie — Mathematische   Begrundung   der 
Iris  Theorie,  Arch,  fiir  Ophthal.  1892. 

Preston,  Theory  of  Light. 

Heath,  Geometrical  Optics. 

Loring,  Ophthalmoscopy. 

Purkinje,     Commentatio     de     Examine    Physiolog.     organi 
Visus,  &c,  1823. 

Tscherning,    Physiologic    Optics,    and    Theorie    de    I'ophtal- 
mometrie  de  la  cornee,  Javal's  Memoires  d'ophtalmometrie. 

Home,  Croonian  Lecture,  Philos.  Trans.,  1796. 
Kohlrausch,  Ueber  die  Messung  des  Radius  der    Vorderjldche 
der  Hornhaut,  Von  Oken's  Isis,  1840. 

Javal,  and  others,  Memoires  d'ophtalmometrie. 

Weiland,  History  and  Principles  of  Keratometry,  Archives 
of  Ophthalmology,  1893. 


no  Principles  of  Optics 

Ettles,  The  Ophthalmometer,  Tr.  Opt.  Soc.  of  London,  1907. 

Sutcliffe,  One  Position   Ophthalmometry,  Tr.  Opt.   Soc.  of 
London,  1907. 


PART  II 

THE    NORMAL    EYE 


CHAPTER  VIII 

THE  REFRACTIVE  MECHANISM 

In  order  that  we  may  investigate  understandingly  the  refrac- 
tive properties  of  the  eye  we  must  be  familiar  with  the  essentials 
of  the  anatomy  of  this  organ. 

The  normal  eyeball  (Fig.  61)  is  nearly  spherical  in  shape. 
The  antero-posterior  diameter  is  the  greatest;  the  vertical 
diameter  is  the  least.  The  former  measures  from  23  mm  to  25 
mm;  the  latter  from  22  mm  to  24  mm.  We  may,  therefore,  with 
sufficient  accuracy  for  a  general  description,  say  that  the  eye- 
ball is  a  globe  whose  diameter  is  about  one  inch. 

If  we  view  the  eye  externally  we  see  that  it  consists  of  two 
distinct  portions :  an  anterior,  transparent  portion,  the  cornea; 
and  a  posterior,  larger,  opaque  portion,  the  sclera.  The  curva- 
ture of  the  cornea  is  greater  than  that  of  the  sclera,  so  that  the 
junction  of  these  two  structures  is  marked  by  a  groove  or  sulcus 
— the  sulcus  of  the  cornea.  Of  an  antero-posterior  meridional 
section  of  the  eyeball,  the  cornea  comprises  about  one-sixth,  and 
the  scleral  portion  the  remaining  five-sixths. 

The  eye  is  protected  posteriorly  by  the  bony  walls  of  the 
orbit,  in  which  it  lies,  but  anteriorly  its  only  protection  is  that 
afforded  by  the  lids.  The  latter  serve,  when  partially  or  com- 
pletely closed,  to  protect  the  eye  from  excessive  light,  and  from 
injury  by  foreign  bodies. 

The  inner  surface  of  the  lids  is  covered  with  mucus- 
membrane,  the  conjunctiva,  which  is  reflected  at  the  upper  and 
lower  fornices  {culs-de-sac)  upon  the  eyeball,  and  the  epithelium 
of  this  membrane  is  continued  over  the  anterior  surface  of  the 

(in) 


112 


The  Normal  Eye 


cornea.  The  conjunctiva  thus  forms  a  sac,  open  anteriorly  at 
the  lid-margins. 

There  are  three  concentric  coats  or  tunics  of  the  eye.  These 
are  called  the  external,  the  middle,  and  the  inner  coat. 

The  External  Coat. — The  external  coat  consists  of  the 
cornea  and  the  sclera.  The  structure  of  these  two  membranes 
is  essentially  the  same,  both  being  composed  of  fibrous  tissue. 


SCM-EMM'S 
CANAL 


eiLunv 

BODY 


FIG.    6 1 

Normal    Fyehall    (diagrammatic) ;    Section    in    the    Horizontal    Meridian. 


The  transparency  of  the  cornea  results  from  the  close  union 
and  regular  arrangement  of  the  fibers,  and  from  the  homogeneous 
composition  of  its  tissues. 

The  cornea  is  covered  anteriorly  with  epithelium  which  is 
continuous  with  that  of  the  conjunctiva.  Immediately  behind  the 
epithelium  is  the  anterior  limiting  membrane,  Bowman's  mem- 
brane, which  is  a  dense,  structureless  membrane.  Behind  this 
is  the  corneal  tissue  proper,  the  stroma,  which  consists  of 
regularly    arranged    lamellae    of    fibrous    tissue.     Between    the 


The  Refractive   Mechanism  113 

bundles  of  fibers  there  are  lymph  spaces  or  lacunae  which  are 
connected  with  each  other  by  small  canals  or  canaNculi.  Each 
lacuna  contains  a  cell  whose  processes  extend  along  the  canaliculi 
to  neighboring  cell-processes,  so  that  there  is  a  general  inter- 
communication between  the  various  cells.  These  cells  are  called 
the  fixed  cells  of  the  cornea,  in  contradistinction  to  the  movable 
cells  or  leucocytes,  which  are  carried  through  the  lymph 
channels.  The  fourth  layer  of  the  cornea  is  D  esc  erne  t's 
membrane,  a  thin,  homogeneous,  resistant  structure,  which  is  a 
part  of  the  middle  coat  of  the  eye.  The  fifth  and  last  layer  of 
the  cornea  is  the  layer  of  endothelium  or  polygonal  cells,  which, 
like  the  preceding,  is  a  part  of  the  middle  coat  of  the  eye. 

There  are  no  blood  vessels  in  the  healthy  cornea ;  nourish- 
ment is  supplied  by  the  lymph  channels. 

The  corneal  nerves  are  derived  from  the  ciliary  plexus. 
They  form  a  network  around  the  corneal  margin  from  which 
branches  are  given  off  to  supply  the  several  layers  of  the  cornea. 

The  sclera  differs  in  structure  from  the  cornea  in  that  its 
fibers  are  irregularly  arranged.  It  is  of  a  white,  glistening  color, 
which  shows  that  its  blood  supply  is  scanty.  The  sclera  is 
pierced  by  a  number  of  openings  for  blood  vessels  and  nerves. 
The  largest  of  these,  which  is  for  the  entrance  of  the  optic  nerve 
and  retinal  vessels,  is  about  1.5  mm  in  diameter.  It  is  situated 
slightly  to  the  nasal  side  of  the  posterior  pole  of  the  eye.*  This 
opening  is  traversed  by  connective  tissue  fibers,  the  lamina 
cribosa.  The  outer  layers  of  the  sclera  are  continuous  with  the 
sheath  of  the  optic  nerve. 

The  greatest  thickness  of  the  sclera  is  in  the  region  of  the 
posterior  pole,  where  a  thickness  of  1  mm  is  attained.  From 
this  region  it  becomes  thinner  towards  the  equator,  and  it  is 
again  thickened  anteriorly  where  the  sclera  is  blended  with  the 
insertions  of  the  ocular  muscles. 

Near  the  sclero-corneal  junction,  and  concentric  with  it, 
there  is  a  circular  canal,  Schlemm's  canal,  which  is  a  venous 
channel. 

The  sclera  is  covered  externally  by  a  thin  layer  of  loose 
connective  tissue,  the  episclera,  which  is  more  freely  supplied 
with  blood  vessels  than  is  the  sclera  itself. 

*The   points   where   the   optic   axis   intersects   the   circumference   of   the   eyeball    are 
regarded  as  the  poles. 


ii4  The  Normal  Eye 

The  anterior  portion  of  the  sclera  is  covered  by  conjunctiva; 
the  posterior  portion  is  embedded  in  a  fibrous  capsule  (Tenon's 
capsule),  in  which  it  is  freely  movable. 

The  Uvea. — The  middle  coat  is  called  the  uvea,  from  its 
resemblance,  when  stripped  from  the  sclera,  to  a  grape. 

The  iris  or  anterior  portion  of  the  uvea  is  a  diaphragm  which 
has  at  or  near  its  center  a  circular  opening,  the  pupil,  for  the 
passage  of  light  to  the  retina.  From  the  pupillary  border  the 
iris  extends  peripherally  to  the  ciliary  body,  to  which  it  is 
attached  at  a  short  distance  behind  the  sclero-corneal  junction. 
The  angle  between  the  sclero-cornea  and  the  iris  is  bridged  over 
by  loose  spongy  tissue  which  is  called  the  ligamentum  pectinatum. 
The  patulency  of  this  structure  is  of  great  importance  in  the 
regulation  of  intraocular  tension,  for  it  is  through  its  meshes 
that  the  aqueous  humor  is  drained  into  Schlemm's  canal,  of 
which  the  ligamentum  pectinatum  forms  the  inner  wall. 

The  iris  is  composed  of  an  endothelial  layer  in  front,  a 
pigment  layer  behind,  and,  between  these  two  layers,  the  stroma. 
The  stroma  is  a  net-work  of  blood  vessels,  and  fibrous  tissue, 
in  which  are  embedded  the  two  muscles  of  the  iris,  the  sphincter 
and  the  dilator  pupillae.  The  former  is  a  circular  band  of  fibers 
about  i  ;//;;/  in  width,  which  surrounds  the  pupil  and  causes  con- 
traction of  this  opening.  The  dilator  muscle  consists  of  radial 
fibers  which  assist  in  dilating  the  pupil. 

The  bluish  color  of  the  iris  in  blondes  is  caused  by  light 
reflected  from  the  pigment  contained  in  the  posterior  or  pigment 
layer.  In  dark  eyes  there  is  also  pigment  in  the  stroma  of 
the  iris. 

The  ciliary  body,  or  middle  portion  of  the  uvea,  is  a  ring- 
shaped  body,  which  surrounds  the  inner  surface  of  the  sclera, 
extending  from  the  sclero-corneal  junction  backward  for  about 
2  mm,  where  it  becomes  merged  with  the  choroid.  This  body, 
which  is  of  importance  in  the  study  of  accommodation,  will  be 
more  fully  considered  in  connection  with  that  subject. 

The  choroid  is  that  part  of  the  uvea  which  is  posterior  to 
the  ciliary  body.  Its  color  is  dark  brown ;  it  thus  differs  from 
the  ciliary  body,  the  inner  surface  of  which  is  black. 

The  choroid  is  a  very  thin  membrane,  being  only  about  .1  mm 
at  its  thickest  part,  which  is  near  the  optic  nerve.     In  structure 


The  Refractive   Mechanism 


115 


it  consists  of   a  net-work   of  blood   vessels,   connective   tissue, 
and  pigment. 

The  blood  supply  is  derived  from  the  anterior  and  posterior 
ciliary  arteries.  After  circulating  through  the  capillaries  the 
blood  leaves  the  eye  through  the  venae  vorticosae,  of  which  there 
are  from  four  to  six  penetrating  the  sclera  in  the  equatorial 
region. 


fig.  62 

Diagram  of  the  structure  of  the  human  retina  according  to  Golgi's  method.    (Greeff.) 

I,  Pigment  layer;  II  and  III  (1  neuron),  the  neuro-epithelial  layer;  IV,  V,  VI, 
VII,  and  VIII  (2  neuron),  the  bipolar  cells,  and  other  cells  whose  function  is  un- 
known;  IX   and  X    (3   neuron),   ganglion   cells   and  nerve   fibers. 


The  nerves  of  the  uvea  are  branches  of  the  long  and  short 
ciliary  nerves.  The  long  ciliary  nerves  are  derived  from  the 
nasal  branch  of  the  fifth  nerve.  The  short  ciliary  nerves  arise 
from  the  ciliary  ganglion.  They  contain  motor  fibers  from  the 
third  nerve,  sensory  fibers  from  the  fifth,  and  sympathetic  fibers 
from  the  sympathetic  system. 

The  Retina. — The  third  or  inner  eye  tunic  is  called  the 


Ii6  The   Normal   Eye 

retina.  It  is  formed  by  the  expansion  of  the  optic  nerve.  The 
nerve  fibers  within  the  eye  consist  only  of  transparent  axis- 
cylinders,  except  in  the  anomalous  condition  of  opaque  nerve 
fibers.  The  fibers  radiate  from  the  optic  disk  or  entrance  of  the 
nerve  so  as  to  form  the  inner  layer  of  the  retina.  The  optic  disk 
is  situated  slightly  to  the  nasal  side  of  the  posterior  pole  of  the 
eye.  The  area  which  the  disk  covers  constitutes  Mario tte's 
blind  spot,  there  being  at  this  place  no  terminal  elements  capable 
of  exciting  vision. 

The  macula  lutca  or  yellow  spot,  situated  about  3  mm  to  the 
outer  side  of  and  a  little  below  the  optic  disk,  is  an  annular 
or  elliptical  area  from  1  mm  to  2  mm  in  diameter.  At  its  center 
there  is  a  minute  depression,  the  fovea  centralis. 

The  retina  extends  forward  as  far  as  the  ora  serrata,  beyond 
which  it  is  rudimentary.  In  the  latter  condition  it  furnishes  the 
posterior  pigment  layer  of  the  ciliary  body  and  iris,  which  is  con- 
tinuous with  the  pigment  layer  of  the  retina. 

In  structure  the  inner  tunic  consists  of  the  supporting 
neuroglia,  or  sustentacular  tissue  of  Miiller,  and  the  retina 
proper.  The  latter  is  composed  of  two  laminae;  an  outer  pigment 
layer,  and  an  inner  layer  of  nerve  tissue.  The  nerve  tissue  is 
divided  into  the  ncuro-epithclial  layer  and  the  cerebral  layer. 

The  neuro-epithelial  layer  consists  of  the  retinal  rods  and 
cones,  which  form  the  light-receiving  and  transforming 
mechanism. 

The  cerebral  layer,  by  which  the  impulse  received  by  the 
rods  and  cones  is  transmitted  to  the  brain,  contains  a  layer  of 
bipolar  cells,  a  layer  of  ganglion  cells,  and  nerve  fibers.  The 
bipolar  cells  connect  the  rods  and  cones  with  the  ganglion  cells 
of  the  nerve  fibers.  They  thus  form  a  connecting  link  between 
the  peripheral  recipient  elements  and  the  conducting  nerve 
fibers  (Fig.  62). 

The  macula  lutea.  so  called  from  its  yellow  appearance  when 
anatomically  examined,  is  the  part  of  the  retina  which  is  con- 
cerned in  distinct  vision.  In  this  region  the  rods  are  replaced  by 
cones,  the  latter  being  much  more  numerous  than  in  other  parts 
of  the  retina.  The  depression  at  the  fovea  centralis  is  due  chiefly 
to  the  thinning  of  the  nerve  fiber  layer  (ganglion  cells)  and 
to  the  sessile  character  of  the  bipolar  cells. 


The  Refract izc   Mechanism  117 

The  blood  sxtpply  of  the  outer  layers  of  the  retina  is  derived 
from  the  capillaries  of  the  adjacent  choroid.  The  inner  layers 
are  supplied  by  the  branches  of  the  central  artery  of  the  retina. 
The  veins  which  carry  the  blood  from  the  retina  follow  the  same 
general  course  as  the  retinal  arteries.  There  are  no  large  vessels 
at  the  macula  (Fig.  63),  but  this  region  is  richly  supplied  with 
capillaries,  except  at  the  fovea,  where  there  are  no  vessels. 


fig.  63 

Blood-vessels   of  the   retina    (Henle). 

Contents  of  the  Eyeball. — There  are  enclosed  by  the 
tunics  of  the  eye  the  aqueous  humor,  the  crystalline  lens,  and  the 
vitreous  body.  These  substances  serve  to  distend  the  tunics 
so  as  to  give  shape  to  the  eyeball,  and  at  the  same  time 
they  serve  as  refractive  media.  As  we  are  concerned  with  them 
chiefly  as  refractive  media  they  will  be  described  as  such  under 
the  following  caption. 

Surfaces  and  Media  of  the  Eye. — As  we  have  already 
learned,  the  anterior  surface  of  the  cornea  is  the  most  effective 
of  the  refracting  surfaces  of  the  eye.  The  form  of  this  surface 
has  been  very  carefully  studied  by  many  investigators  since  the 
introduction  of  ophthalmometry  by  Helmholtz.  As  the  measure- 
ment of  this  surface  with  Helmholts's  ophthalmometer  was  a 
laborious  procedure,  the  number  of  observations  was  not  nearly 
so  great  as  have  been  more  recently  made  with  the  Javal- Schiotz 
instrument.  Prior  to  the  invention  of  this  ophthalmometer  it 
was  customary  to  regard  the  normal  cornea  as  resembling  the 


n8  The   Normal  Eye 

small  end  of  an  ellipsoid  as  formed  by  revolution  about  its  long 
axis.  The  measurements  which  had  been  made  were  sufficient 
to  show  that  the  cornea,  like  the  ellipsoid,  had  a  greater  curvature 
at  the  center  than  at  the  periphery.  But  when  more  numerous 
measurements  at  various  distances  from  the  center  were  after- 
ward made  with  the  Javal-Schiotz  ophthalmometer,  it  was  learned 
that  the  cornea  as  a  whole  could  not  be  compared  to  any  sym- 
metrical surface. 

The  following  conclusions  have  been  reached  by  Sulzer  as 
to  the  form  of  the  cornea : 

(a)  The  central  region  of  the  normal  cornea  differs  but  little 
from  a  segment  of  a  sphere. 

(b)  At  a  distance  of  about  2  mm  from  the  point  of  inter- 
section of  the  visual  line  with  the  cornea  the  curvature  begins 
abruptly  to  diminish.  From  this  point  to  its  periphery  the  corneal 
surface  shows  a  progressively  decreasing  curvature. 

(c)  Whether  we  regard  the  point  of  intersection  of  the 
visual  line  with  the  corneal  surface,  or  the  point  of  maximum 
curvature  as  representing  the  center  of  the  cornea,  the  curva- 
ture does  not  diminish  proportionally  to  the  distance  from  this 
center.  This  is  true  whether  the  distance  is  measured  on  the 
two  principal  meridians  or  on  the  two  halves  of  the  same 
meridian;  in  other  words,  the  cornea  is  not  in  any  sense  a  surface 
of  symmetrical  curvature. 

The  average  radius  of  curvature  of  the  central  portion  of 
the  cornea  is,  according  to  H elm-holt z,  7&2.Q  mm.  Other  averages 
do  not  differ  materially  from  this,  and  a  radius  of  7.8  mm  may 
be  accepted  as  the  standard  for  the  normal  eye.  The  limits 
within  which  the  radius  varies  in  emmetropia  are  comprised 
(as  determined  by  Schiotz  from  a  large  number  of  examinations) 
between  7.2  mm  and  8.6  mm.  The  variations  of  curvature  in  a 
number  of  measurements  by  Tscherning  are  shown  graphically 
in  Fig.  64. 

The  curvature  of  the  posterior  surface  of  the  cornea  follows, 
in  general,  that  of  the  anterior  surface,  but  it  approximates  some- 
what more  nearly  the  spherical  form.  The  average  radius  of 
curvature,  as  ascertained  by  anatomists  and  by  Tscherning,  is 
6  mm. 

The  thickness  of  the  central  portion  of  the  cornea  is  about 
1  mm  (Tscherning  and  others). 


The  Refractive  Mechanism  119 

The  refractive  index  of  the  cornea,  as  determined  by  Aubert, 
is   I.377.     Other  estimates  differ  but  slightly  from  this. 

Hehnholtz,  in  his  schematic  eye,  adopted  1.3365  as  the 
common  index  of  cornea,  aqueous,  and  vitreous. 

The  distance  of  the  retina  from  the  anterior  surface  of  the 
cornea  in  this  schematic  eye  is  22.8  mm;  whereas  in  my  calcula- 


8.43mm 
fig.  64 

The  abscissas  indicate  the  radii  of  curvature  of  the  cornea  in  millimeters,  the 
ordinates  the  number  per  hundred  of  emmetropes  in  whom  we  meet  the  radius  of 
curvature     (Tscherning). 

tion,  which   is  based   upon    four   refractions,   the   corresponding 
distance  from  the  cornea  to  the  retina  is  23.2  mm. 

The  aqueous  humor  occupies  the  space  (the  anterior 
chamber)  between  the  cornea  and  the  crystalline  lens.  The 
aqueous,  being  fluid,  must  be  enclosed  in  a  solid  receptacle 
in  order  that  its  index  may  be  determined.  A  small  quantity 
of  the  aqueous  may  be  placed  at  the  apex  of  two  inclined  plates 
of  glass;  or  it  may  be  enclosed  in  a  hollow  lens  {Hehnholtz). 
The  refractive  effect  of  the  glass  being  known,  the  remaining 
refraction  which  occurs  in  the  passage  of  light  through  the  com- 
bination represents  the  effect  of  the  aqueous  humor,  from  which 
the  index  can  be  derived  by  calculation.  The  index,  as 
determined  by  Hehnholtz,  is  1.3365;  Fleischer  gives  1.3373 
as  the  average  index.  An  index  of  1.337  may  be  accepted 
as  the  standard. 


120  The   Normal   Eye 

The  transparency  of  the  cornea  and  aqueous  humor,  as  direct 
inspection  shows,  is  almost  perfect.  This  transparency  is 
attained  in  the  cornea  by  the  great  regularity  and  close  union  of 
the  individual  lamellae,  and  by  the  interposition  of  a  cement 
substance  of  the  same  index  as  that  of  the  lamellae ;  otherwise 
reflection  from  the  various  strata  would  interfere  with  the 
passage  of  light.  In  health  it  is  only  by  the  most  careful  exami- 
nation that  we  are  able  to  detect  any  such  reflection,  but  when 
the  physiological  arrangement  is  disturbed  by  disease,  the  cornea 
loses  its  transparency. 

Much  greater  difficulty  has  been  experienced  in  determining 
the  exact  form  of  the  surfaces  of  the  crystalline  lens  than  in 
determining  the  form  of  the  cornea ;  but  measurements  made  by 
Helm  holts,  Donders,  Knapp,  and  others — which  have  recently  been 
substantiated  by  Tscheming — show  that,  the  ciliary  muscle  being 
relaxed,  the  central  portion  of  the  anterior  surface  does  not 
materially  differ  from  a  segment  of  a  sphere  having  a  radius 
of  io  mm,  and  that  the  corresponding  portion  of  the  posterior 
surface  equally  resembles  a  segment  of  a  sphere  having  a  radius 
of  6  mm*  Since  only  the  central  portions  of  these  surfaces  are 
concerned  in  normal  vision,  we  may  in  our  calculations  assume 
that  they  are  spherical. 

From  a  number  of  anatomical  measurements,  made  prior  to 
the  era  of  ophthalmometry,  Briicke  concluded  that  the  anterior 
surface  of  the  lens  corresponded  approximately  with  the  surface 
generated  by  the  revolution  of  an  ellipse  about  its  minor  axis, 
while  the  posterior  surface  approximated  a  paraboloid  of  revo- 
lution. Although  neither  surface  is  a  true  geometrical  curve, 
Briicke's  conclusions  have,  in  general,  been  justified  by  measure- 
ments made  by  Tscheming  and  others,  inasmuch  as  these 
measurements  show  that  the  anterior  surface  presents  its  least 
curvature  near  the  axis  (when  the  eye  is  in  relaxation),  and  that 
the  posterior  surface  has  its  greatest  curvature  near  the  axis  with 
a  slight  diminution  at  the  periphery. 

The  average  axial  distance  of  the  anterior  surface  of  the 
cornea  from  the  anterior  surface  of  the  crystalline  lens  is  3.6  mm, 


*These  are  average  measurements.  The  anterior  surface  of  the  lens  has,  in  the 
measurements  which  I  have  made,  varied  between  9  mm  and  11.5  mm  (approximately); 
and  the  radius  of  the  posterior  surface  has  varied  between  5.5  mm  and  7.5  mm.  Even 
these  extensive  limits  have  been  passed  in  the  recorded  measurements  of  Hclmholtz 
and  others. 


The  Refractive  Mechanism 


121 


as  determined  by  Helmholtz.    The  thickness  of  the  cornea  being" 
regarded  as  I  mm,  the  depth  of  the  anterior  chamber  is  2.6  mm. 

The  average  thickness  of  the  lens,  according  to  Helmholtz, 
is  3.6  mm;  according  to  Merkel,  it  is  t>-7  nun;  Tscheming 
gives  4.1  mm.  The  lack  of  agreement  between  these  figures  is 
doubtless  due  in  part  to  the  fact  that,  on  account  of  the  difficulty 
of  observation,  the  number  of  individuals  examined  by  each 
investigator  was  not  large  enough  to  establish  a  correct  average ; 
but  it  seems  certain  that  Helmholtz 's  estimate  is  too  low.  A 
thickness  of  4  mm  (Listing)  may  be  accepted  as  the  standard 
for  the  normal  eye. 


FIG.    65 

Section  of  the   Crystalline   Lens    (Sernoff). 

The  total  or  equivalent  index  of  the  lens  may  be  derived 
with  approximate  accuracy  by  determining  the  indices  of  the 
outer,  intermediate,  and  nuclear  layers,  and  by  calculating  there- 
from the  refractive  power  of  a  lens  composed  of  these  layers. 
These  determinations  have  been  made  by  a  number  of  investi- 
gators with  fairly  close  approximation  to  uniformity.  According 
to  Woinow  the  average  index  of  the  adult  lens  is  1.4386. 
Fleischer  assigns  1.4371  as  the  equivalent  index,  which  was 
adopted  by  Helmholtz  in  his  later  schematic  eye.  A  more  recent 
estimation  by  Stadfelt  assigns  1.435  as  tne  equivalent  index. 

Listing  (and  Helmholtz  in  his  first  schematic  eye)   adopted 


122  The   Normal  Eye 

the  fraction  |f  (1.4545)  as  the  index  of  the  lens.  That  this 
is  too  high  is  evidenced  by  the  insufficient  length  (22.2  mm)  of 
Listing's  schematic  eye. 

T scheming  adopts  1.42,  which,  on  the  other  hand,  is 
apparently  too  low,  since  the  length  of  the  eye  as  determined 
by  calculation  with  this  index  is  longer  than  the  emmetropic  eye 
as  measured  by  anatomists. 

For  the  purpose  of  calculation  an  index  of  1.437  mav  be 
accepted  as  the  average  for  the  normal  eye.  Assigning  this  index 
to  the  lens,  and  1.337  as  the  index  of  the  aqueous  and  vitreous, 
we  determine  from  calculation  that  the  crystalline  lens  {in  situ) 
has  a  focal  length  of  about  51  mm.  If  we  could  disregard  the 
thickness  of  the  lens  this  focal  length  would  correspond  to  a 
dioptric  power  of  19.5  D ;  but  that  we  cannot  without  error 
disregard  the  thickness  is  apparent  from  the  application  of  the 
formula  for  conjugate  foci.  We  find  that  a  lens  of  about  14.5  D, 
placed  at  the  anterior  surface  of  the  crystalline  lens,  would, 
in  conjunction  with  the  corneal  refraction,  bring  parallel  rays  to 
a  focus  on  the  imaginary  retina  of  the  schematic  eye.  If,  on  the 
other  hand,  the  imaginary  thin  lens  is  placed  at  the  posterior 
surface  of  the  crystalline  lens,  it  must  have  a  power  of  about 
21.5  D.  If  we  place  the  lens  2  mm  behind  the  anterior  surface  of 
the  crystalline  lens — between  its  two  nodal  points — the  required 
power  is  about  17.5  D,  which  we  may,  with  as  near  an  approxi- 
mation to  accuracy  as  is  possible,  regard  as  the  dioptric  equivalent 
of  the  normal  crystalline  lens. 

The  crystalline  lens,  composed  of  fibers  (Fig.  65),  is 
divisible  into  three  principal  segments,  and  it  not  infrequently 
happens  that  in  a  healthy  eye  the  indices  of  these  separate 
segments  are  not  quite  uniform.  From  this  there  results  a  condi- 
tion of  irregular  astigmia — a  defect  which,  in  fact,  exists  to 
some  extent  in  all  eyes. 

The  transparency  of  the  lens  is  rendered  imperfect  by  its 
heterogeneity  of  structure.  Reflection  from  the  interfibrillar  sub- 
stance and  from  the  lines  of  union  of  the  segments  of  the  lens 
can,  under  favorable  circumstances,  be  observed  in  the  examina- 
tion of  an  eye. 

We  may  observe  the  shadows  (the  lens-spectrum)  which 
defects  of  transparency  cause  to  fall  upon  our  own  retinas.  We 
may  do  this  most  readily  by  admitting  to  the  eye,  in  a  dark  room, 


The  Refractive   Mechanism 


123 


a  beam  of  light  which  is  diffused  upon  the  retina  by  a  strong 
convex  or  concave  lens  ( 15  D)  placed  as  near  as  possible  to  the 
eye,  as  in  a  trial  frame.  The  light  from  a  lamp  may  be  reflected 
into  the  eye  by  the  surface  of  another  strong  lens  obliquely 
inclined  {N orris),  or  by  the  ordinary  concave  forehead  mirror. 
The  examination  of  the  lens-spectrum  shows  numerous  opacities 
which  would  not  otherwise  be  suspected   (Fig.  66). 


fig.  66 

Lens   Spectrum.    {Bonders.) 

The  lens  becomes  less  transparent  in  old  age,  and  some- 
times assumes  a  yellowish  hue.  This  physiological  loss  of 
transparency  does  not  materially  interfere  with  vision,  but  in  a 
certain  proportion  of  cases  a  still  further  change  occurs — an 
infiltration  between  the  fibers — whereby  the  lens  loses  its  trans- 
parency and  becomes  cataractous. 

In  old  age  there  is  usually  an  increasing  density  of  the 
cortex,  which  makes  the  whole  lens  approach  homogeneity,  the 
effect  being  a  diminution  of  the  refracting  power  of  the  lens. 
On  the  other  hand,  a  pathological  swelling  of  the  nucleus  which 
is  frequently  the  precursor  of  cataract,  may  increase  the  refrac- 
tive power  and  produce  myopia. 

The  vitreous  body  fills  the  greater  part  of  the  cavity  of  the 
eyeball — all  that  part  which  is  back  of  the  crystalline  lens. 


124  The   Normal  Eye 

The  refractive  index  of  the  vitreous  is  determined  in  the 
same  way  as  is  that  of  the  aqueous.  All  estimates  agree  in 
assigning  indices  so  nearly  identical  for  these  two  media  that 
they  may  be  regarded  as  identical  for  the  purpose  of  calculation. 

The  transparency  of  the  vitreous  body  seems  perfect  when 
examined  in  the  normal  eye  with  the  ophthalmoscope,  but  by 
looking  at  a  uniformly  bright  light,  as  the  sky,  it  is  possible  to 
see  shadows  which  opacities  in  this  substance  cast  upon  our  own 
retinas.  These  opacities  are  due  to  connective  tissue  cells  and 
leucocytes  which  float  in  the  vitreous.  They  are  called  muscae 
volitantes,  because  they  appear  as  flies  flitting  before  the  face. 
They  do  not  interfere  with  vision  except  when  in  disease  a  patho- 
logical multiplication  of  these  cells  takes  place. 

Insensitiveness   of   the    Periphery   of   the    Retina. — In 

refraction  by  a  series  of  surfaces  it  is  only  in  the  vicinity  of  the 
primary  optic  axis  that  well  defined  images  are  formed.  The 
insensitiveness  of  the  peripheral  portions  of  the  retina  is  a  provi- 
sion of  nature  which  prevents  our  noticing  the  diffused  condition 
of  the  images  as  they  are  formed  at  a  considerable  distance  from 
the  optic  axis.  Although  the  field  of  vision  in  a  healthy  eye  is 
large,  it  is  within  a  very  small  part  of  this  field  that  a  clear  visual 
impression  of  an  external  object  is  received.  If  an  object  lying 
within  this  field  of  indistinct  vision  attracts  attention,  the  eye  is 
at  once  turned  by  its  muscular  apparatus  into  the  proper  position 
to  receive  a  clear  image. 

The  fovea  centralis,  upon  which  falls  the  image  of  every 
object  attracting  the  visual  attention,  does  not  exceed  0.4  mm 
in  diameter. 

We  see,  therefore,  that  that  part  of  the  retinal  image  which 
is  utilized  in  distinct  vision  is  extremely  small ;  and  we  must 
not  think  that  vision  is  properly  represented  by  the  diagrams 
which  we  often  see  having  the  image  pictured  as  covering  a  large 
part  of  the  retina.  We  see  the  various  parts  of  an  object  by 
rapidly  changing  the  visual  attention  from  one  part  to  another. 
The  eye  is  constantly  in  motion,  bringing  the  image,  first  of  one 
part  of  the  object  and  then  of  another  upon  the  fovea. 

Alpha  and  Gamma. — If  the  eye  is  a  well  constructed 
optical  apparatus,  the  fovea  centralis  must  lie  at  or  near  the  inter- 
section of  the  axis  and  the  retina.    As  a  matter  of  fact  the  fovea 


The  Refractive   Mechanism  125 

always  lies  near  the  axis,  but  seldom  upon  it.  It  is  apparent 
therefore  that  the  nodal  ray  which  joins  the  fovea  with  the  point 
looked  at  does  not  coincide  with  the  primary  axis  of  the  eye. 

This  is  shown  in  an  exaggerated  degree  in  Fig.  67,  in  which 
F  F'  is  the  optic  axis  and  V  V  is  the  nodal  ray  joining  the  fovea 
and  the  point  to  which  the  visual  attention  is  directed.  The 
point  V  is  called  the  point  of  fixation,  and  the  line  V  V  is  called 
the  visual  line. 

The  angle  which  the  visual  line  makes  at  the  nodal  point  with 
the  optic  axis  is  the  angle  alpha  (a)  of  Bonders.  This  angle 
varies  considerably   in  different  persons.     As  a  rule  the   fovea 


fig.  67 

Angle  Alpha — Alpha  is  represented  by  A   N   V,  or  by  F'  N'   V. 

(F')lies  farther  from  the  optic  disk  than  the  focus  {F')t  and 
consequently  the  visual  line  intersects  the  cornea  on  the  nasal 
side  of  the  optic  axis.  This  is  called  the  positive  angle  alpha. 
When,  as  less  frequently  happens,  the  visual  line  intersects  the 
cornea  on  the  temporal  side,  alpha  is  said  to  be  negative.  In  the 
horizontal  meridian  alpha  is  usually  not  more  than  five  degrees 
in  conditions  approximating  emmetropia.  In  the  vertical  meridian 
it  is  seldom  more  than  two  or  three  degrees,  the  visual  line  lying 
above  the  optic  axis. 

Alpha  is  greatest  in  hyperopia,  and  least  in  myopia.  In  the 
latter  condition  alpha  is  sometimes  negative.  Bonders  gives  seven 
and  one-half  degrees  as  the  average  of  this  angle  in  the  higher 
degrees  of  hyperopia.    Very  rarely  it  may  reach  ten  degrees. 

To  measure  the  angle  alpha  we  place  the  electric  lamps  of 
the  ophthalmometer  in  the  meridian  at  right  angles  to  that  in 
which  we  wish  to  determine  the  angular  displacement  of  the  lens. 
We  then  note  the  angle  which  the  visual  line  makes  with  the  axis 
of  the  telescope  when  the  images  reflected  from  the  anterior 
surface  of  the  cornea  and  from  the  two  surfaces  of  the  crystalline 


126  The   Normal   Eye 

lens  are  in  alignment.  In  order  that  the  images  reflected  from 
the  two  surfaces  of  the  lens  may  be  seen  simultaneously  an 
instrument  of  long  focal  length  is  required,  such  as  Tscheniiug's 
ophthalmo-phakometer. 

Sometimes  it  will  be  found  impossible  to  bring  all  three 
images  into  alignment.  In  such  cases  there  is  a  defect  of  center- 
ing ;  the  three  surfaces  have  no  common  axis.  Absolute  exactness 
is  not  to  be  expected,  but  ordinarily  the  deviation  from  a  correct 
centering  is  slight. 

Although  the  images  from  all  three  surfaces  cannot  be  seen 
simultaneously  with  an  instrument  of  short  focal  length,  we  can 
measure  with  such  an  instrument  the  angle  alpha  with  sufficient 
accuracy  for  practical  purposes  by  bringing  into  alignment  the 
images  as  reflected  from  the  cornea  and  from  the  posterior 
surface  of  the  lens. 

The  angle  which  Donders  called  alpha  has  been  called 
gamma  (  y  )  by  Landolt,  who  has  characterized  as  alpha 
the  angle  which  the  imaginary  long  axis  of  the  corneal  ellipse 
makes  with  the  visual  line.  The  measurements  of  Tscheming 
and  others  have  shown  that  the  summit  of  corneal  curvature 
seldom  lies  at  a  noteworthy  distance  from  the  optic  axis ;  practi- 
cally therefore  the  angles  alpha  and  gamma  of  Landolt  may  be 
regarded  as  identical,  and  either  of  them  may  be  regarded  as 
expressing  the  angular  distance  between  the  visual  line  and  the 
optic  axis. 

The  Iris. — The  iris  has  already  been  described  as  an  adjust- 
able diaphragm  which  is  placed  just  in  front  of  the  anterior 
surface  of  the  lens.  The  pupil,  through  which  light  passes  to 
the  retina,  is  at  or  near  the  center  of  the  iris,  usually  slightly  to 
the  nasal  side.  The  peripheral  rays  of  light  which  are  most 
affected  by  the  optical  imperfections  of  the  eye,  are  thus  pre- 
vented from  reaching  the  retina. 

The  size  of  the  pupil  is  regulated  by  the  sphincter  and 
dilator  muscles  of  the  iris.  Stimulation  of  the  retina  by  a  bright 
light  produces  by  reflex  action  a  contraction  of  the  pupil.  When" 
this  stimulus  is  removed  during  feeble  illumination  the  pupil 
dilates  so  as  to  permit  more  light  to  enter  the  eye. 

The  pupil  also  contracts  consensually  with  accommodation 
and  convergence. 


The  Refractive  Mechanism  127 

The  apparent  size  of  the  pupil  as  we  see  it  is  somewhat 
larger  than  the  actual  size,  since  it  is  magnified  by  refraction 
as  the  rays  from  its  border  leave  the  cornea.  Its  diameter 
appears  about  one-eighth  larger  than  it  really  is. 

We  cannot  fix  any  definite  size  of  the  normal  pupil,  since 
this  varies  with  the  degree  of  illumination,  and  also  with  different 
individuals  under  the  same  conditions.  The  pupil  is  larger  in 
early  life  and  becomes  notably  smaller  in  old  age.  The  average 
diameter  of  the  pupil  in  ordinary  daylight  is  usually  regarded  as 
being  about  4  mm. 

Choroidal  and  Retinal  Pigment. — The  inner  surface  of 
a  photographic  camera  is  blackened  for  the  purpose  of  absorbing 
all  extraneous  light.  In  the  eye  the  pigment  of  the  choroid  and 
retina  performs  this  function,  thus  preventing  internal  reflec- 
tions with  consequent  marring  of  images. 

REFRACTION  OF  THE  EYE 

The  refraction  of  the  eye  is  the  expression  which  we  use 
in  ophthalmology  to  indicate  the  relation  between  the  position 
of  the  retina  and  the  posterior  principal  focus  of  the  dioptric 
system  of  the  eye. 

The  static  refraction  expresses  this  relation  as  it  exists 
during  complete  relaxation  of  the  ciliary  muscle.  By  the  term 
dynamic  refraction  we  express  the  power  of  increasing  the 
refractive  action  which  the  eye  possesses  in  the  accommodative 
contraction  of  the  ciliary  muscle.  When  the  term  refraction  of 
the  eye  is  used  without  qualification  it  refers  to  the  static 
refraction. 

Emmetropia. — When  the  principal  focus  lies  at  the  inter- 
section of  the  optic  axis  and  retina  during  relaxation  of  the 
ciliary  muscle,  the  eye  is  adapted  to  receive  a  clear  image  of  a 
distant  object.  This  is  the  ideal  eye.  It  is  regarded  as  the 
normal  type  of  the  human  eye,  and  it  is  called  the  emmetropic 
eye.* 

Nature  approximates  but  seldom  attains  emmetropia,  and 
it  is  evident  that  the  more  the  methods  of  measurement  are 
refined    the    less    will    be    the    proportion    of    eyes    regarded    as 


•The  word  "emmetropia"  was  derived  by  Donders  from  the  Greek  €(i(i€TpOS    (iu  due 

measure)  and  »y  (eye  or  vision). 


128  The  Normal  Eye 

emmetropic.  We  must  therefore  assign  limits  within  which  the 
emmetropic  eye  may  vary.  These  limits  are  determined  practi- 
cally by  the  weakest  lenses  (plus  and  minus)  in  the  complete 
trial  case.  We  regard  an  eye  as  emmetropic  when  the  weakest 
lens  of  the  trial  case  does  not  bring  the  retina  and  focus  into 
greater  proximity  than  they  are  without  the  lens. 

Axial  Length  of  the  Emmetropic  Eye. — It  is  not  within 
the  range  of  probabilities  that  individaul  normal  eyes  should 
present  uniformity  either  of  curvature  or  of  axial  length; 
but,  as  the  researches  of  Helmholtz  and  others  show  that  the 
curvature  varies  only  within  comparatively  small  limits,  so  also 
anatomical  examination  of  eyes  which  were  known  to  be 
emmetropic,  or  nearly  so,  shows  that  their  axial  length  varies  to 
a  correspondingly  slight  extent. 

The  distance  from  the  anterior  surface  of  the  cornea  to  the 
retina,  as  determined  by  my  calculation,  is  23.22  mm.  The 
thickness  of  the  choroid  and  sclera  in  the  region  of  the  macula 
is  about  1  mm;  theoretically,  therefore,  the  antero-posterior 
diameter  of  the  normal  eye  should  be  24.22  mm  in  length.  That 
it  does  not  in  fact  deviate  much  from  this  average  is  attested 
by  anatomists,  who  find  the  length  of  the  normal  eye  to  vary 
between  23  mm  and  25  mm.  Merkel  assigns  24.3  mm  as  the 
average  length;  Sappey  (average  of  28  eyes  of  both  sexes),  24.2 
mm;  Macalcstcr's  Anatomy  (1889),  24.27  mm;  Morris's  Anatomy 
(1894),  24.5  mm,  and  Quain's  Anatomy  C1894),  24  mm. 

These  measurements  apply  to  the  eyes  of  adults.  The  eyes 
of  infants  and  young  children  are  notably  smaller  than  the  eyes 
of  grown  persons.  Although  the  smallness  of  the  eyes  in 
childhood  is  a  physiological  condition,  such  eyes  are  usually 
hyperopic,  and  their  consideration  belongs  to  the  chapter  devoted 
to  that  condition. 

Accommodation 

In  emmetrop'a  the  macula  lutea  coincides  with  the  posterior 
principal  focal  plane  of  the  eye,  and  the  eye,  if  otherwise  normal, 
fulfils  the  conditions  necessary  to  receive  a  clear  image  of  a 
distant  object.  But  the  image  of  a  near  object  would  be  formed 
at  its  conjugate  focal  plane,  behind  the  posterior  principal  focal 
plane,  and  since  light  would  be  intercepted  by  the  retina  before 
reaching  this  conjugate  focal  plane,  the  rays  from  any  point  of 


The  Refractive  Mechanism  129 

the  object,  not  having  reached  their  intersecting  point,  would 
form  upon  the  retina  a  diffusion-circle.  The  image  of  the  object, 
being  an  aggregation  of  such  diffusion-circles,  would  be 
blurred. 

In  order  to  overcome  the  indistinctness  of  vision  which 
would  result  from  these  diffusion  images,  we  make  use  of  the 
power  of  accommodation,  as  far  as  this  is  available. 

The  mechanism  of  accommodation,  the  means  by  which  we 
are  enabled  to  adapt  the  eye  for  different  distances,  has  engaged 
the  attention  of  physicists  for  more  than  three  hundred  years;  it 
has  been  the  subject  of  many  writings  and  of  much  contention. 
The  celebrated  astronomer  Kepler,  who  was  the  pioneer 
student  of  the  dioptrics  of  the  eye  (1611),  sought  to  account 
for  the  power  of  accommodation  by  postulating  a  change  in  the 
length  of  the  eye — a  change  which  he  thought  might  be 
accomplished  by  muscular  compression.* 

Scheiner  (1619)  described  the  pupillary  contraction  which 
occurs  in  accommodation,  and  suggested  that  changes  might  also 
occur  in  the  crystalline  lens,  but  Des-Cartes  (1637)  is  usually 
regarded  as  the  originator  of  the  idea  of  an  increase  of  convexity 
of  this  lens. 

The  first  definite  proof  that  accommodation  is  due  to  an 
increase  of  convexity  of  the  crystalline  lens  was  given  by  Young 
(1801).  There  were  three  credible  hypotheses  for  the  expla- 
nation of  accommodative  action:  (a)  that  it  was  accomplished 
by  increase  of  curvature  of  the  cornea;  (b)  by  increase  of  curva- 
ture of  the  crystalline  lens;  and  (c)  by  elongation  of  the  eyeball. 

Young  proved  (1)  that  there  was  no  increase  of  curvature 
of  the  cornea  during  accommodation  and  (2)  that  the  eyeball 
was  not  elongated.  He  proved  the  first  proposition  by  observing 
the  images  reflected  from  the  cornea,  and  also  by  immersing  his 
eye  in  water  in  such  a  way  that  the  refractive  action  of  the  cornea 
was  eliminated  and  replaced  by  a  convex  spherical  lens.  In 
order  to  prove  that  there  was  no  elongation  of  the  eyeball  he 
took  advantage  of  the  fact  that  he  had  very  prominent  eyes. 
By  turning  the  eye  as  far  as  possible  inward,  and  by  inserting 
a  small  ring  between  the  bone  and  the  posterior  polar  region 


"The  statement  made  by  Helniholts  and  subsequent  writers  that  Kepler  believed 
accommodation  to  be  accomplished  by  a  to-and-fro  movement  of  the  crystalline  lens 
is  erroneous. 


130  The   Normal  Eye 

of    the    eye    he    proved    that    his    accommodative    power    was 
unaffected,  although  it  was  impossible  for  the  eye  to  elongate. 

Young  also  proved  by  means  of  his  optometer  that  persons 
who  had  been  operated  on  for  cataract  had  no  power  of  accommo- 
dation. He  therefore  firmly  established  that  this  power  resided 
in  the  crystalline  lens,  and  therefore  that  it  could  only  result  from 
an  increase  in  the  curvature  of  this  lens. 

As  the  nature  of  the  ciliary  muscle  was  at  that  time  not 
known,  Young  was  unable  to  give  a  rational  explanation  of  the 
means  by  which  the  change  of  curvature  was  accomplished. 

It  is  said  that  Young's  work  attracted  but  little  attention  at 
the  time  and  that  it  was  only  after  the  renewed  study  of  this 
subject  nearly  fifty  years  later  that  his  experiments  were 
accredited. 

The  fact  that  accommodation  is  accomplished  by  an  increase 
of  curvature  of  the  crystalline  lens  was  first  actually  demonstrated 
by  Langenbeck  in  1849,  who  observed  the  changes  in  the  images 
formed  by  reflection  at  the  anterior  surface  of  the  lens.  A  little 
later  (in  1851)  Cramer  constructed  a  magnifying  instrument  with 
which  he  could  better  observe  these  images,  and  he  was  able 
to  demonstrate  very  clearly  the  movement  of  the  images  which 
occurred  in  accommodation.  Finally  Helmholtz  by  the  invention 
and  application  of  his  ophthalmometer  was  enabled  to  measure 
the  size  of  the  image  as  formed  at  the  posterior  as  well  as  that 
at  the  anterior  surface  of  the  lens.  He  was  therefore  able  to 
measure  the  amount  of  increase  of  curvature  which  took  place. 
He  observed  that  while  by  far  the  greater  part  of  the  accommo- 
dation was  due  to  the  increased  curvature  of  the  anterior  surface, 
there  was  also  a  slight  change  of  curvature  of  the  posterioi 
surface. 

From  his  investigations  Helmholtz  concluded  that,  10  mm 
being  the  average  radius  of  curvature  of  the  anterior  surface 
of  the  crystalline  lens  during  relaxation,  6  mm  is  the  average 
radius  during  maximum  accommodation  in  young  adults;  that 
the  radius  of  the  posterior  surface  of  the  crystalline  lens  changes 
from  an  average  of  6  mm  to  an  average  of  5.5  mm;  and  that  the 
thickness  of  the  lens  increases  from  3.6  mm  to  4  mm,  with  a 
corresponding  advance  of  the  anterior  surface.  These  conclusions 
of  Helmholtz  have  been  universally  accepted,  as  regards  all  but 


The  Refractive   Mechanism  131 

the  increased  thickness  of  the  lens,  which  Tscherning  thinks  has 
not  been  definitely  proved. 

The  Ciliary  Region. — The  lens,  whose  general  form  and 
size  have  already  been  described,  is  fibrillar  in  structure  and 
varies  in  consistency  according  to  the  age  of  the  individual.  In 
infancy  the  entire  lens-substance  is  of  a  soft  semifluid  or  gela- 
tinous nature ;  but  with  increasing  age  the  central  or  nuclear 
portion  gradually  becomes  firmer  in  consistency.  By  the  time 
adult  life  is  reached  the  nucleus  has  become  weakly  solidified. 
This  hardening  process  continues  so  that  the  nucleus  increases  in 
size  and  hardness  as  the  maturity  of  the  individual  advances. 
The  outer  or  cortical  portion  also  increases  in  firmness,  and  in 
old  age  the  entire  lens  is  transformed  into  a  solid  mass,  with  a 
nucleus  of  still  greater  hardness. 

The  lens  substance  is  enclosed  in  a  delicate,  transparent,  and 
contractile  capsule. 

The  lens,  enclosed  in  its  capsule,  is  supported  in  its  position 
between  the  iris  and  aqueous  humor  on  one  side  and  the  vitreous 
body  on  the  other  by  a  delicate  ligament — the  zonule  of  Zinn,  or 
suspensory  ligament  of  the  lens.  This  ligament  is  attached  to 
the  anterior  and  posterior  surfaces  of  the  capsule  near  the  equator 
or  peripheral  border  of  the  lens  (Fig.  61). 

The  ligament,  thus  attached  to  the  lens,  has  its  outer  border 
attached  to  the  ciliary  processes  and  to  the  depressions  between 
these  processes.  Opposite  to  the  equator  of  the  lens,  about  .5  mm 
distant  and  projecting  anteriorly,  lie  the  ciliary  processes,  a 
network  of  blood  vessels  and  pigment  which  line  the  inner  circum- 
ference of  the  sclero-corneal  ring,  and  which,  extending  back- 
ward, become  united  with  the  choroid. 

The  muscular  character  of  the  ciliary  body  was  discovered  by 
Wallace,  an  American  physician,  in  1836.  As  American  litera- 
ture was  at  that  time  little  known  in  Europe,  Wallace's  discovery 
received  practically  no  attention,  and  later  Bowman  in  England 
and  Briicke  in  Germany  described  the  muscle  at  about  the  same 
time  (1847). 

The  ciliary  muscle  lies  beneath  the  ciliary  processes.  It  is 
composed  of  non-striated  fibers  and  consists  of  two  parts.  The 
larger  portion  is  formed  of  meridional  fibers,  usually  called 
Briicke 's  muscle,  which  are  attached  anteriorly  with  firm  union  to 
the  sclero-corneal  junction  and  neighboring  part  of  the  sclera. 


132  The   Normal  Eye 

The  libers  of  this  part  of  the  muscle,  passing  backward,  are  in- 
serted into  the  anterior  portion  of  the  choroid.  This  is  the  most 
external  part  of  the  muscle,  its  outer  surface  being  in  contact 
with  the  sclera.  On  the  inner  side  of  the  meridional  fibers 
and  adjoining  the  ciliary  processes  is  the  second  or  transverse 
part  of  the  muscle,  ordinarily  known  as  the  annular  muscle  of 
Muller.  This  consists  of  a  circular  band  of  fibers  surrounding 
the  margin  of  the  iris.  Some  of  the  fibers,  after  proceeding  for 
a  certain  distance  transversely,  penetrate  this  part  of  the  muscle 
and  join  the  first  or  meridional  portion. 

In  emmetropia  the  proportion  in  size  of  the  two  divisions 
of  the  muscle  is  about  ten  of  the  first  to  one  of  the  second; 
while  in  hyperopia  the  circular  portion  is  more  abundant,  and 
in  myopia  it  is  less  so  or  even  absent  (Iwanoff). 

The  sphincter  of  the  iris  and  the  ciliary  muscle  are  innervated 
by  the  third  nerve,  acting  through  the  ciliary  ganglion.  These 
muscles  are  therefore  involuntary  in  their  action;  contraction 
occurs  as  the  result  of  reflex  stimulation.  We  have  no  control 
over  the  pupillary  movements,  but  to  a  certain  extent  we  can 
cultivate  the  power  of  voluntarily  contracting  and  relaxing  the 
ciliary  muscle. 

Helmholtz's  Theory. — It  was  Helmholtz  also  who,  after 
demonstrating  the  changes  which  occur  in  the  lens  during  accom- 
modation, first  presented  a  rational  explanation  of  the  way  in 
which  these  changes  are  accomplished.  He  assumed  that,  the 
anterior  extremity  of  the  ciliary  muscle  being  attached  to  the 
firm  sclero-corneal  junction,  contraction  of  this  muscle  would 
draw  forward  the  anterior  portion  of  the  choroid,  to  which  the 
posterior  extremity  is  attached.  In  consequence  of  this  forward 
motion  the  ciliary  processes  and  the  suspensory  ligament  of  the 
lens  would  also  be  drawn  forward,  and  relaxation  of  this  ligament 
would  occur. 

If  we  assume,  with  Helmholtz,  that  this  relaxation  and 
forward  movement  actually  occur,  we  need  only  to  glance  at 
our  illustration  (Fig.  68),  and  to  bear  in  mind  the  constitution 
of  the  lens  in  order  to  understand  what  will,  in  a  general  way, 
be  the  effect  of  this  relaxation  upon  the  shape  and  position  of 
the  lens. 

In  childhood,  at  which  period  accommodation  is  most  active, 


The  Refractive  Mechanism 


133 


the  lens  consists  of  a  semifluid  or  gelatinous  mass  enclosed  in  a 
contractile  capsule.  The  tendency  of  such  a  mass  is  to 
approximate  the  spherical  form.  This  is  because  a  fixed  volume 
of  matter  presents  its  smallest  area  of  external  surface  when  in 
this  form,  and  what  is  known  in  physics  as  the  surface-tension 


fig.  68 

The  crystalline  lens  and  ciliary  region.     The  dotted  outline   represents  the  change 
which   occurs  in  accommodation. 


of  the  mass  and  also  the  contractility  of  the  capsule  are  ever 
acting  to  reduce  this  surface-area.  A  simple  illustration  of 
this  is  afforded  by  a  thin  rubber  bag  distended  with  water.  If 
by  pressure  or  traction  on  the  bag  the  shape  is  altered,  its  original 
form  will  at  once  be  resumed  on  release  from  pressure. 


134  The  Normal  Eye 

Although  the  tendency  of  such  a  body  is  to  assume  the 
spherical  form,  there  may  be  a  number  of  counterbalancing  forces 
which  prevent  this  form  from  being  attained.  In  the  case  of  the 
rubber  bag,  for  instance,  the  structure  of  the  latter  may  be  such 
as  to  give  an  oval  form  to  the  body.  Similarly,  in  the  lens 
there  are  modifying  conditions,  resulting  from  its  characteristic 
structure,  and  even  if  no  external  traction  were  exercised,  a 
perfectly  spherical  form  would  not  be  assumed. 

In  its  normal  position  in  the  eye  the  pressure  or  traction  by 
the  suspensory  ligament  causes  the  lens  to  assume  an  ovoidal 
form.  We  observe  that  the  anterior  part  of  this  ligament  is 
shorter  than  the  part  which  is  attached  to  the  posterior  surface 
of  the  lens,  and  that,  as  a  result  of  this,  the  tension  is  greater 
upon  the  anterior  than  upon  the  posterior  surface.  As  the  tension 
is  greater  upon  the  anterior  surface,  so  the  effect  of  relaxation 
must  be  greater  upon  this  than  upon  the  posterior  surface. 
Hence,  if  the  lens  has  not  become  solidified  in  its  flattened  form, 
relaxation  of  the  ligament  allows  the  anterior  surface  to  advance 
with  a  decided  increase  of  curvature.  The  effect  of  relaxation 
of  the-  posterior  portion  of  the  ligament  being  less  marked,  the 
posterior  surface  undergoes  only  slight  increase  of  curvature  with 
no  measurable  change  of  position. 

Experimental  Observations. — The  first  experimental 
observations  made  for  the  purpose  of  ascertaining  whether  the 
changes  which  take  place  in  accommodation  agree  with  the 
assumption  of  Helmholtz  were  undertaken  by  Hensen  and 
Voelckcrs.  Their  experiments,  which  were  made  upon  the 
lower  animals,  consisted  in  exposing  the  ciliary  ganglion  and 
ciliary  region,  and  observing  the  changes  caused  by  irritation  of 
the  ciliary  nerves.  By  this  means  they  were  able  to  demonstrate : 
(i)  contraction  of  the  pupil  with  a  forward  motion  of  the  pupil- 
lary border  of  the  iris,  and  of  the  anterior  surface  of  the  lens, 
with  an  increase  of  curvature  of  this  surface;  (2)  contraction  of 
the  ciliary  muscle  with  advancement  of  the  ciliary  processes  and 
anterior  portion  of  the  choroid. 

The  changes  which  occur  in  the  living  human  eye  in  accom- 
modation were  investigated  by  Coccins  (1867)  and  later  by 
Hjort.  Coccius  observed  eyes  upon  which  peripheral  iridectomies 
had  been  performed,  and  Hjort  made  use  of  a  person  in  whom 
there  existed  total  aniridia,  the  result  of  accident.     The  changes 


The  Refractive  Mechanism  135 

which  these  investigators  were  able  to  detect  resembled  those 
which  have  been  described  by  Hensen  and  Voelckers  as  occurring 
in  lower  animals.  Coccius  and  Hjort  were  further  enabled  to 
view  the  ciliary  region  directly  and  to  demonstrate  that  the 
ciliary  processes  advance  during  accommodation.  Since,  as  these 
processes  advance,  they  also  become  more  prominent,  the  investi- 
gators were  led  to  believe  that  the  efferent  veins  from  this 
region  were  compressed,  and  that,  in  consequence,  there  was  an 
increase  of  intra-ocular  pressure.  Subsequent  investigations, 
however,  have  shown  that  there  is  no  such  increase  of  pressure 
during  accommodation. 

Resting  upon  these  demonstrations,  Helmholtz's  theory  of 
accommodation  has  received  almost  universal  acceptance,  but  its 
correctness  has  been  denied  by  several  able  investigators. 

Tscherning's  Theory. — Tscherning,  who  is  the  chief 
advocate  of  the  counter-theory  that  accommodation  is  produced, 
not  by  relaxation  but  by  increased  tension  of  the  suspensory 
ligament,  gives  the  following  reasons  for  rejecting  Helmholtz's 
theory : 

"(1)  The  increase  of  refraction  of  the  lens  in  accommo- 
dation takes  place  only  near  the  apex  of  the  lens.  This  is 
established  by  study  of  the  spherical  aberration  of  the  eye. 
Aberration,  which  is  positive  when  the  eye  is  at  rest,  diminishes 
or  even  becomes  negative  in  maximum  accommodation. 

"(2)  Measurements  with  the  ophthalmo-phakometer  show 
that  the  increase  of  curvature  of  the  anterior  surface  of  the  lens 
is  confined  to  the  portion  near  the  summit  of  the  lens,  and  that 
the  anterior  surface  does  not  move  forward,  but  remains  station- 
ary or  moves  slightly  backward. 

"(3)  Experiments  made  upon  the  eyes  of  animals  show  that 
traction  upon  the  ligament  of  the  lens  produces  an  increase  of 
curvature  near  the  summits  of  the  surfaces,  and  relaxation  pro- 
duces diminution  of  curvature." 

Helmholtz  confined  his  measurements  to  the  portion  of  the 
surfaces  near  the  optic  axis,  but  Tscherning  has  investigated 
the  curvature  of  more  peripheral  parts  of  the  lens-surfaces.  He 
has  found  that  the  curvature  of  the  anterior  surface,  which  plays 
the  more  important  part  in  accommodation,  diminishes  very 
rapidly  as  the  distance  from  the  axis  increases,  and  he  concludes 
that  the  anterior  surface  of  the  lens  assumes  in  accommodation 


136 


The  Normal  Eye 


a    form    closely    approximating  a  hyperboloid,  a  form  which  he 
believes  inconsistent  with  Helmholtz's  theory. 

The  researches  of  Tscherning  make  it  necessary  for  us  to 
modify  our  conception  of  the  change  which  takes  place  in  the 
crystalline  lens  in  accommodation,  but  they  do  not   require  us 


a  fig.  69  b 

Lens   of   a   Calf, 
(a)      Under     relaxation     of     the     suspensory     ligament;     (b)     Under     traction     of 
the   ligament. 

to  abandon  the  theory  of  Helmholtz  that  the  increase  of  curvature 
results  from  a  relaxation  of  the  zonula  of  the  lens.*  It  is  far 
easier,  in  my  opinion,  to  reconcile  the  form  of  curvature  as 
Tscherning  finds  it  with  Helmholtz's  theory  than  it  is  to  believe 
that  this  change  can  be  produced  by  traction  of  the  zonula. 


■■ 


a  FIG.  70  b 

Lens  of  an  Ox 
(a)    Under    relaxation;    (b)    Under    traction    of    the    ligament. 

Some  years  ago  I  repeated  T  scheming' s  experiments,  using 
lenses  of  the  calf  as  well  as  of  the  mature  ox.f  When  using  the 
lenses  of  the  young  animal  I  was  not  in  any  case  able  to  obtain 
an  increase  of  curvature  by  traction   (Fig.  69).     In  the  case  of 


*In  fact  it  is  apparent  from  Helmholtz's  illustrations  that  he  did  not  assume 
the  existence  of  the  spheroidal  curvature  of  the  lens  in  accommodation.  This  mis- 
conception arose  in  subsequent  descriptions. 

t  Theory    of   Accom.,    Arch,    of   Ophth.    XXIX. 


The  Refractive  Mechanism 


137 


the  ox,  however,  I  found  that  the  lenses  were  composed  of  a  center 
or  nucleus  of  great  hardness  surrounded  by  soft  material.  By 
making  traction  on  lenses  of  this  kind  I  obtained  an  increase  of 
curvature  (Fig.  70).  It  is  easy  to  understand  why  this  results 
with  the  hard  nucleus,  but  this  nucleus,  upon  which  7 'scheming 's 
theory  is  based,  does  not  exist  in  childhood,  the  age  of  greatest 
accommodative  activity.  Furthermore,  even  if  we  should  concede 
that  the  lens  might  assume  the  accommodation  form  under  trac- 


a 


fig.  71 


tion  of  the  zonular  ligament  (Fig.  71,  a),  we  should  still  find 
difficulty  in  believing  that  this  form  could  be  continuously  main- 
tained in  the  soft  lens  of  a  young  person.  The  prolonged 
traction  of  the  ligament  would,  after  a  time  varying  with  the 
hardness  of  the  nucleus  produce  a  flattening  of  the  latter  with  a 
diminution  of  the  total  curvature  (Fig.  71,  b). 

Another  matter  upon  which  T scheming  lays  great  stress 
has  little  weight  in  support  of  his  argument.  He  says  that  if 
Helmholtz's  theory  is  correct  we  ought  to  find  the  lenses  of  dead 
persons  in  a  state  of  maximum  curvature  when  we  remove  the 
lenses  from  their  attachments.     We  should  not,  however,  expect 


138  The   Normal  Eye 

this,  for  with  the  loss  of  the  body  heat  the  lenses  become  hard 
and  do  not  readily  undergo  a  change  of  shape. 

For  anatomical  information  in  regard  to  the  accommoda- 
tion curvature  of  the  human  lens  we  must  depend  upon  eyes 
enucleated  from  living  persons,  and  it  is  not  often  that  we  have 
an  opportunity  of  examining  normal  lenses  in  this  way.  I  have 
had  this  opportunity  only  once.  In  that  instance  I  examined  at 
the  moment  of  enucleation  of  the  eye  a  healthy  lens  of  a  man 
twenty-five  years  of  age.  When  I  removed  the  lens  from  the 
eye  I  observed  that  the  usual  flattened  aspect  of  the  anterior 
surface  was  absent;  in  fact  the  shape  of  this  surface  very  closely 
resembled  the  accommodation  form  described  by  Tscherning. 
Moreover,  traction  made  at  opposite  points  of  the  equator  pro- 
duced a  decided  flattening  of  curvature,  which  disappeared  on 
release  from  traction.  The  action  of  the  lens  did  not  in  any  way 
justify  a  belief  in  Tscherning  s  theory.  Finally,  a  gentle  mas- 
saging of  the  lens  (in  its  capsule)  between  the  fingers,  which 
destroyed  its  characteristic  structure,  resulted  in  the  lens  assum- 
ing a  spherical  shape  when  released  from  pressure. 

The  foremost  antagonist  of  Tscherning's  theory  is  Hess, 
who  has  conducted  experiments  to  prove  that  the  suspensory  liga- 
ment is  in  a  relaxed  condition  during  accommodation.  The 
experiments  of  Hess  consisted  chiefly  in  demonstrating:  (1)  the 
correctness  of  the  observations  of  Coccius  and  Hjort;  (2)  a 
sinking  of  the  lens  from  gravity  when  the  eye  makes  a  maximum 
effort  of  accommodation;  and  (3)  a  change  of  position  of  the 
lens  during  accommodation  with  change  of  position  of  the  head ; 
that  is,  a  forward  motion  with  the  head  inclined  forward  (down- 
ward) and  a  backward  motion  with  the  head  thrown  back. 

A  brief  but  very  clear  description  of  these  experiments,  as 
given  by  Professor  Hess  himself  in  an  address  before  the  Ameri- 
can Medical  Association,  may  be  found  in  the  reports  of  the 
Ophthalmological  Section  for  the  year  1907. 

In  view  of  these  facts  and  notwithstanding  the  plausible  and 
ably  presented  arguments  of  Tscherning,  I  believe  that  we  should 
hold  to  Helmholtzs  theory  of  a  relaxed  zonula,  unless  this  theory 
should  be  rendered  untenable  by  more  conclusive  evidence  than 
has  hitherto  been  adduced  against  it. 

Length  of  Time  Required  for  Accommodation. — 
Experiments  have  been  conducted  for  the  purpose  of  ascertain- 


The  Refractive  Mechanism  139 

ing  how  long  a  period  of  time  is  required  for  the  production 
and  relaxation  of  accommodation.  As  a  result  of  these  experi- 
ments it  is  stated  that  it  requires  from  one  to  two  seconds  to 
change  the  adaptation  from  the  distance  adjustment  to  the  usual 
reading  position,  and  about  one-half  of  this  period  to  produce  the 
inverse  change.  The  length  of  time  required  for  these  acts  varies 
in  different  persons  and  at  different  ages,  a  greater  time  being 
required  as  the  crystalline  lens  becomes  more  solid  in  consistency. 

Range  of  Accommodation. — Since  the  solidity  of  the  lens 
undergoes  a  gradual  increase  from  infancy  to  old  age,  it  follows 
that  the  power  of  this  lens  to  assume  greater  convexity  under  the 
relaxing  influence  of  the  ciliary  muscle  must  suffer  a  gradual 
diminution  with  advancing  years.  At  ten  years  of  age,  the 
youngest  period  of  life  at  which  accommodation  can  well  be 
measured,  the  normal  eye  can  accommodate  for  a  point  about  70 
mm  from  the  eye;  at  twenty  years  of  age  the  nearest  point  for 
which  the  eye  can  accommodate  is  100  mm;  at  forty-five  years  the 
nearest  point  is  about  250  mm;  and  at  seventy  years  little  or  no 
accommodative  power  ordinarily  remains. 

The  nearest  point  for  which  an  eye  can  accommodate  is 
called  the  near  point  ( punctum  pro.rimum,  p.  p.). 

The  dioptric  equivalent  of  the  accommodative  power  of  an 
eye  is  called  the  amplitude  or  range  of  accommodation. 

The  following  table  gives  Donders's  estimate  of  the  range  of 
accommodation  of  the  eye  at  different  ages. 

Age   10  15  20   25  30   35   40   45   50   55  60   6.«  70     75 

Diopters*  14   12   10  8.5   7  5.5  4.5  3.5  2.5  1.75   1  0.75  0.25   o 

While  the  range  of  accommodation  is  the  same  in  ametropia 
(except  in  high  degrees)  as  in  emmetropia,  the  position  of  the 
near-point  varies  with  the  state  of  refraction.  Thus,  in  an 
emmetropic  eye  which  has  4  D  of  accommodation  the  far-point 
is  at  infinity  and  the  near-point  is  at  a  distance  of  one-fourth 
of  a  meter  from  the  eye.  In  the  case  of  a  hyperopic  eye  a  certain 
amount  of  accommodation  must  be  exercised  to  procure  distinct 
distant  vision,  and  only  what  remains  is  available  for  near  vision. 
If  in  an  eye  having  4  D  of  accommodation  there  is  hyperopia  of 
2  D,  only  2  D  will  remain  for  adapting  the  eye  to  near  vision,  and 
the  near-point  is  one-half  of  a  meter  from  the  eye. 


'Adapted  from  the  inch  system  by   Landolt. 


140  The  Normal  Eye 

The  far-point  of  the  hyperopic  eye  is  negative — that  is,  only 
convergent  pencils  can  be  focused  on  the  retina  without  accommo- 
dation; but  as  no  convergent  pencils  enter  the  eye  (except  by 
previous  refraction),  the  negative  part  of  the  range  of  vision  is 
of  no  use  in  ordinary  vision,  and  practically  the  far-point  of  the 
hyperopic  eye  lies  at  infinity.  Hence,  in  the  aforementioned  case 
the  range  of  vision  is  from  infinity  to  a  point  one-half  of  a  meter 
from  the  eye. 

If,  on  the  other  hand,  there  is  myopia  of  2  D,  the  far-point 
lies  at  a  distance  of  one-half  of  a  meter  from  the  eye.  Beyond 
this  point  distinct  vision  is  not  possible;  but  for  near  vision,  if 
this  eye  can  command  4  D  of  accommodation  in  addition  to  the 
2  D  of  myopia,  its  lens-equivalent  is  in  all  6  D.  The  near-point 
of  distinct  vision  is,  therefore,  one-sixth  of  a  meter  from  the 
eye,  and  the  range  of  vision  embraces  only  the  interval  lying 
between  these  two  points,  distant,  respectively,  500  mm  and  167 
mm  from  the  eye. 

The  emmetropic  eye  requires  4  D  of  accommodation  to  see 
distinctly  at  a  distance  of  one- fourth  of  a  meter;  the  eye  having 
2  D  of  hyperopia  requires  6  D;  and  the  eye  having  2  D  of  myopia 
requires  2  D  of  accommodation  for  vision  at  this  distance. 

It  will  be  noticed  that  while  1  D  of  accommodation  will 
change  the  adaptation  of  the  eye  from  infinity  to  a  point  one 
meter  from  the  eye,  an  additional  diopter  will  effect  a  change 
from  one  meter  to  one-half  of  a  meter  only,  and  another  addi- 
tion of  one  diopter  will  change  the  adjustment  from  a  point  one- 
half  of  a  meter  distant  to  a  point  one-third  of  a  meter  from  the 
eye.  Thus  we  see  that  as  an  object  approaches  the  eye  the  amount 
of  accommodation  required  for  distinct  vision  increases  at  a 
rapidly  increasing  rate. 

Reserve  Accommodation. — It  is  not  possible  for  anyone 
to  use  all  his  accommodative  power  for  a  prolonged  period  of 
time.  Investigations  by  Landolt  have  shown  that  about  one-third 
of  this  power  must  be  held  in  reserve,  if  continuous  work  is  to  be 
done.  A  person  having  just  3  D  of  accommodative  power  could 
not  read  continuously  at  33  cm;  in  order  for  him  to  do  this  he 
must  have  at  least  4.5  D  at  his  disposal,  for  he  must  keep  in 
reserve  1.5D  (1/3  of  4.5  D),  leaving  3  D  for  actual  use. 


The  Refractive  Mechanism  141 

The  following  authorities  have  been  consulted  in  the  prepara- 
tion of  the  foregoing  chapter. 

Baker,  Anatomy  of  the  Eye,  Norris  and  Oliver's  System  of 
Diseases  of  the  Eye. 

Gray,  Anatomy. 

Morris,  Anatomy. 

Macalester,  Anatomy. 

Quain,  Anatomy. 

Merkel,  Topographische  Anatomic 

Sappey,  Traite  d'anatomie. 

Greeff",  Der  Ban  der  menschlichen  Retina,  Magnus,  Augen- 
artz.     Unterrichtstafeln. 

Henle,  Grundriss  der  Anatomie  des  Menschen. 

Babuchin  (Sernoff)  The  Lens,  Strieker's  Histology. 

Helmholtz,  Optique  Physiologique,  and  Ueber  die  Accommo- 
dation des  Auges,  Arch,  fur  Opht,  1855. 

Donders,  Anomalies  of  Refraction  and  Accommodation. 

Landolt,  Refraction  and  Accommodation  of  the  Eye. 

Aubert,  Dioptrik  des  Auges,  Graefe — Saemisch,  1st  ed. 

Knapp,  Die  Kriimmung  der  Homhaut  des  mensch.  Auges. 

Sulzer,  La   forme   de   la   cornee   humaine   et  son  influence 
sur  la  vision,  Arch,  d'ophtal.,  1891. 

Schiotz,  Untersuchungen  von  969  Augen,  Arch,  fur  Augen- 
heilkunde,  1885. 

Fleischer,    Neue   Bestimmungen   der   Brechungsexponenten 
des  Auges,  1872. 

Woinow,  Uber  die  Brechungscoeff.  der  Verschied.    Linsen- 
schichten,  Klin  Monatsbl'atter  fur  Augenheilkunde,   1874. 

Brucke,  Anat.  Beschreibung  des  menschlichen  Augapfels. 

Kepler,  Dioptrice. 

Scheiner,  Oculus. 

Des-Cartes,  De  Oculo. 

Young,  Mechanism  of  the  Eye. 

Stadfelt,  Recherches  sur  I'indice  total  du  cristallin  humain, 
Jour,  de  Physiologie  et  Pathologie,  1889. 

Norris,  Diseases  of  the  Lens,  Norris  and  Oliver's  System  of 
Diseases  of  the  Eye. 

Listing,  Dioptrik  des  Auges,  Wagner's  Handwoerterbuch  der 
Physiologie. 


142  The  Normal  Eye 

Schauenburg,  Das  Accommodationsvermogen  der  Augen 
nach  Cramer,  1854. 

Langenbeck,  Klin.  Beitrdge  aus  dem  Gebiete  der  Chir.  und 
Ophthal,  1849. 

Coccius,  Der  Mechanismus  der  Accommodation. 

Hjort,  Die  Ciliarfortsdtzc  wdhrend  der  Accommodation,  Klin. 
Monatsblat.  fur  Augenheil,  1876. 

Hensen  und  Voelckers,  Experimentaluntersuchung  uber  den 
Median,  der  Akkom.,  Arch,  fur  Ophthal.  1873. 

Iwanoff,  (Ciliary  Muscle),  Graefe-Saemisch,  1st  ed. 

Hubbell,  Development  of  Ophthalmology  in  America, 
Jour.  A.  M.  A.,  1907. 

Wallace,  A  Treatise  on  the  Eye,  1839. 

Crzellitzer,  Die  Tscherningsche  Accotnmodationstheorie, 
Arch,  fur  Oph.,  1896. 

Tscherning,  Physiologic  Optics. 

Schoen,  Accom.  U  ebcranstrun  gun  g  und  deren  Folgen,  Arch, 
fur  Ophth.,  1887;  and  Der  Accommodationsmechanismus,  Arch, 
fur  Ges.  Phys.,  1895. 

Hess,  Arbeiten  aus  dem  Gebiete  der  Accommodationslehre , 
Arch,  fur  Oph.,  1896-1899;  and  Modern  Views  of  the  Physiology 
and  Pathology  of  Accommodation.  Trans.  A.  M.  A.,  1907;  and 
Refr.  und.  Accom.,  Graefe-Saemisch,  2nd  ed. 

Priestley  Smith,  Demonstration  of  T scheming  s  Theory  of 
Accommodation,  Ophthal.  Review,  1897. 

Grossman,  Mechanism  of  Accommodation,  British  Med. 
Journal,  1903. 

Duane,  Accommodation  and  Donders's  Curve,  Journal  A.  M. 
A.,  1909. 


CHAPTER  IX 


THE  MOTOR  MECHANISM 

The  eyeball  is  much  smaller  than  the  cone-shaped  cavity 
of  the  orbit  in  which  it  is  lodged.  The  space  between  the  eye 
and  the  bony  wall  of  the  orbit  is  filled  with  muscles,  fascia,  cellular, 
and  adipose  tissue.  The  muscles  form  a  cone  similar  in  shape  to 
the  cone  of  the  orbit,  but  smaller.  In  the  hollow  of  this  cone 
the  eye  is  embedded,  the  fascia,  cellular,  and  adipose  tissue  filling 
up  the  rest  of  the  orbital  cavity. 

The  fascia  of  the  orbit  is  well  adapted  for  retaining  the 
eye  in  its  proper  position  and  at  the  same  time  allowing  freedom 
of  motion  about  its  center. 

The  fibrous  sheath  which  surrounds  the  eyeball  was  first 
accurately  described  by  Tenon  (1806),  from  whom  it  takes  its 
name.  This  fascia  extends  from  the  lids  and  periosteum 
anteriorly,  and,  investing  closely  the  eyeball,  extends  posteriorly 
along  the  optic  nerve  to  be  blended  with  the  periosteum  at  the 
apex  of  the  orbit.  It  also  envelops  the  ocular  insertions  of  the 
recti  muscles  and  continues  over  from  one  muscle  to  another,  so 
as  to  form  a  circular  band  of  fibrous  tissue  and  muscular  tendons. 
Strong  ligamentous  bands  are  stretched  between  the  eyeball  and 
the  periosteum  of  the  orbit. 

This  fascia  is  sometimes  called  Bonnet's  capsule  from  a  later 
anatomist  who  described  it  (1841),  and  who  called  attention  to 
the  intimate  adherence  of  the  fascia  to  the  muscular  tendons.  It 
is  because  of  this  adherence  that  we  can  sever  the  tendon  for 
the  correction  of  strabismus  without  entailing  serious  impairment 
of  action  of  the  muscle. 

More  recently  the  orbital  fascia  has  been  the  subject  of  study 
and  description  by  Motais,  whose  plates  have  been  made  use  of 
in  almost  all  recent  text-books  dealing  with  the  ocular  muscles. 

Some  of  these  plates  are  made  with  a  special  view  to 
showing  the  check  ligaments,  the  strong  prolongations  of  fascia 

143 


144 


The  Normal  Eye 


which  extend  between  the  eyeball  and  the  anterior  part 
of  the  orbit  (Fig.  72).  These  ligaments  have  an  important  use  in 
limiting  the  rotations  of  the  eye  and  in  keeping  it  in  its  proper 
position  in  the  orbit. 

The  Extrinsic  Muscles  of  the  Eye. — There  are  attached 
to  the  eyeball  for  the  purpose  of  controlling  its  movements  six 
muscles,   four   recti   and    two    oblique    (Fig.    73).      These    six 


Int.  C.L.,.— 


A.E.C. 


Int.  R..: 


C.L. 


Ext.  R. 


FIG.    72 

Tenon's  Fascia  (from  Motais).  Int.  C.  L.  and  Ext.  C.  L. — Internal  and  External 
Check  Ligaments.  Int.  R.  and  Ext.  R. — Internal  and  External  Recti.  A.  £._  C.  and 
P.  E.  C. — Anterior  and  Posterior  External  Capsule.  /.  C.  L. — Intra-capsular  Ligament, 
or   "Collarette."    /.    C. — Internal   Capsule.      D. — Deep   Layer   of   Muscular    Sheath. 


muscles  are  called  extrinsic  or  extra-ocular  muscles  in  contradis- 
tinction to  the  ciliary  and  iritic  muscles,  which  are  the  intrinsic 
muscles  of  the  eye. 

The  four  recti  muscles  arise  from  the  margin  of  the  optic 
foramen,  and  in  their  course  forward  bound  the  funnel-shaped 
space  in  the  hollow  of  the  basal  portion  of  which  the  eyeball  rests. 

The  internal  rectus  is  attached  anteriorly  to  the  sclera  on  the 
nasal  side  of  the  eye,  about  5  mm  from  the  margin  of  the  cornea. 

The  inferior  rectus  is  similarly  attached  at  the  lower  side  of 
the  sclera,  about  6  mm  from  the  margin  of  the  cornea. 

The  external  rectus  is  attached  at  the  temporal  side,  about  7 
mm  from  the  margin  of  the  cornea. 

The  superior  rectus  is  attached  above,  about  8  mm  from  the 
margin  of  the  cornea. 


The  Motor  Mechanism 


145 


These  are  average  measurements  as  determined  by  Motais. 
They  may  be  easily  remembered,  since  they  correspond  to  the 
consecutive  numbers,  5,  6,  7,  8.  In  the  case  of  the  superior  and 
inferior  recti,  whose  lines  of  insertion  are  obliquely  inclined  to  the 
corneal  margin,  the  measurements  refer  to  the  middle  points  of 
the  attachments. 

The  insertions  of  the  recti  muscles  have  been  diagrammati- 
cally  represented  by  Fuchs  (Fig.  74).  His  measurements  differ 
slightly  but  not  materially  from  those  of  Motais. 

The  internal  rectus  is  most  favorably  attached  for  rotating 
the  eye,  and  the  inferior  rectus  holds  the  second  place  in  this 
respect.  This  is  in  accordance  with  the  physiological  require- 
ments, since  the  greatest  tax  is  imposed  upon  these  two  muscles. 


fig.  73 

Showing  the  origin  and  attachment  of  the  extra-ocular  muscles  and  the  position 
01  the  eyeball  in  the  orbit.  The  letter  T  represents  the  trochlea,  which  is  at  the  inner 
and  upper  angle  of  the  orbit;  E.  R.  represents  the  external  rectus,  /.  R.  the  internal 
and  5.  R.  the  superior  rectus;  S.  O.  represents  the  superior  oblique.  The  inferior 
rectus  and  the  inferior  oblique  are  not  shown.  The  scleral  attachment  of  the 
superior  rectus  is  represented  by  s.  r..  that  of  the  superior  oblique  bv  s.  o.  and  that 
of   the   inferior   oblique   by  t.    o.    (After   Fuchs.) 


The  breadth  of  the  tendons  at  their  lines  of  insertion  is  from 
10  mm  to  11  mm,  except  for  the  inferior  rectus,  the  breadth  of 
which  is  somewhat  less,  from  9  mm  to  10  mm. 

Nerve  Supply  of  the  Extrinsic  Muscles. — The  third  or 
oculomotor  nerve  supplies  all  the  extrinsic  muscles  of  the  eye 
except  the  superior  oblique  and  the  external  rectus.    The  superior 


146 


The  Normal  Eve 


oblique  is  supplied  by  the  fourth,  and  the  external  rectus  by  the 
sixth  nerve. 

Ocular    Motions. — The    eyeball    is    freely   movable    in    all 
directions.     The  primary  position  is  defined  as  that  position  which 


fig.  74 

Diagram   showing   scleral   attachments   of   the    ocular   muscles.    (Fitchs.) 


the  eye  occupies  when,  with  head  erect,  the  visual  attention  is 
directed  straight  forward  at  the  horizon. 

When  the  cornea  is  turned  nasalward  the  eye  is  said  to  be 
adducted;  when  the  cornea  is  turned  temporalward  the  eye  is 
.abducted.  Similarly  upward  rotation  is  called  supraduction  or 
elevation;  downward  rotation  is  subduction  or  depression. 

In  place  of  these  terms  we  may  use  adversion,  abversion, 
supraversion,  and  in  f  raver  sion. 

When  the  eye  rotates  around  its  antero-posterior  axis,  or 
when  the  normally  vertical  meridian  loses  its  vertically  the  eye 
is  said  to  undergo  torsion.  When  the  upper  margin  of  the  cornea 
is  rotated  temporalward  the  torsion  is  called  positive  (also  called 
extorsion)  ;  when  the  upper  margin  of  the  cornea  is  rotated  nasal- 
ward  the  torsion  is  negative  (intorsion). 

The  internal  and  the  external  recti  muscles  form  a  pair; 
both  rotate  the  eye  around  its  vertical  axis.*   The  internal  muscle 


*In  referring  to  the  action   of  the  ocular  muscles  we   mean,   in  general,   the  action 
which  would  be  exerted  when  the  eye  is  in  the  primary  position. 


The  Motor  Mechanism  147 

draws  the  cornea  inward,  or  produces  adduction;  while  the 
external  muscle  draws  the  cornea  outward,  or  produces  abduction. 
The  superior  and  inferior  recti  do  not  form  a  pair  of  muscles 
acting  in  the  same  plane,  as  do  the  internal  and  external  recti. 
This  is  because  of  the  divergence  of  the  orbits.  When  the  eye 
is  in  the  primary  position,  contraction  of  the  superior  rectus  will 
draw  the  cornea  upward  {sit production  ),  but  it  will  also  draw  it 
inward,  and  will  produce  an  inward  rotation  (around  the 
antero-posterior  axis )  of  the  upper  border  of  the  cornea. 
If  the  eye  has  been  previously  adducted  by  contraction  of 
the  internal  rectus,  these  subsidiary  functions  of  the  superior 
rectus  will  be  increased;  but  if  on  the  other  hand  the 
eye  has  been  previously  abducted  by  contraction  of  the  external 
rectus  the  subsidiary  actions  will  be  diminished,  and  when  the 
antero-posterior  axis  lies  in  the  plane  of  muscular  action,  the 
superior  rectus  will  act  as  a  simple  elevator  of  the  cornea  (Fig. 


fig.  75 

Showing    the    effect    of    abduction    upon    the    action    of    the    superior    or    inferior 
rectus    (Fit c lis). 

75).    In  still  greater  abduction  subsidiary  actions  opposite  to  those 
which  have  been  described  arise. 

As  the  chief  function  of  the  superior  rectus  is  to  draw  the 
cornea  upward,  so  the  chief   function  of  the  inferior  rectus   is 


148  The  Normal  Eye 

to  draw  the  cornea  downward,  but  the  subsidiary  actions  of  the 
two  muscles  do  not  lie  in  the  same  plane ;  for  when  the  eye  is 
in  the  primary  position  contraction  of  the  inferior  rectus  not 
only  draws  the  cornea  inward,  but  at  the  same  time  it  rotates  the 
lower  margin  of  the  cornea  inward.  As  with  the  superior  rectus, 
these  subsidiary  actions  are  greatest  when  the  eye  is  adducted, 
and  they  vanish  when  the  eye  is  so  abducted  that  the  antero- 
posterior axis  lies  in  the  plane  of  muscular  action. 

The  superior  and  inferior  recti  make  about  the  same  angle 
with  the  median  plane.  This  angle  varies  in  different  persons. 
The  average  as  determined  by  Fuchs  is  23  °.  Other  authorities 
give  a  somewhat  larger  angle  as  the  average,  about  27  °. 

The  superior  oblique  muscle  draws  the  cornea  downward 
and  outward  and  at  the  same  time  it  rotates  the  upper  margin 
of  the  cornea  inward.  The  last  of  these  motions  is  greatest  when 
the  eye  is  in  abduction,  and  it  diminishes  in  adduction. 

The  superior  oblique  counteracts  the  subsidiary  effects  of 
the  inferior  rectus,  so  that  by  the  combined  action  of  these  two 
muscles  the  cornea  may  be  drawn  directly  downward. 

The  inferior  oblique  draws  the  cornea  upward  and  outward 
and  rotates  the  upper  margin  of  the  cornea  outward.  The  last 
motion  is  greatest  in  abduction  and  least  in  adduction. 

The  inferior  oblique  acts  in  conjunction  with  the  superior 
rectus  and  by  counteracting  the  subsidiary  effects  of  the  latter, 
it  permits  the  cornea  to  be  drawn  directly  upward. 

It  is  probable  that  an  important  function  of  the  two  oblique 
muscles  is  to  counteract  the  backward  pull  of  the  recti  muscles. 
The  eye,  being  thus  properly  poised,  rotates  freely  without  dis- 
placement. 

Center  of  Rotation. — It  has  not  been  absolutely  demon- 
strated that  the  eye  has  a  fixed  center  of  rotation  for  all  motions, 
but  if  there  is  a  change  of  center  it  is  slight.  Several  methods  have 
been  used  to  find  this  center.  The  method  of  Donders  and  Dojer 
is  usually  accepted  as  being  the  most  reliable.  In  the  application 
of  their  method  these  investigators  first  measured  the  diameter 
of  the  cornea  with  an  ophthalmometer.  They  then  suspended  a 
fine  hair  in  front  of  and  close  to  the  cornea,  and  examined  the 
angle  through  which  the  eye  turned  in  order  to  bring  first  one 
and  then  the  other  border  of  the  cornea  directly  behind  the  hair 
as  seen  by  the  examiner  in  the  telescope.     From  this  angle  and 


The  Motor  Mechanism  149 

from  the  diameter  of  the  cornea  they  deduced  the  position  of  the 
center  of  rotation. 

This  method  has  been  criticised  because  the  position  of  the 
center  of  rotation  is  assumed  in  measuring  the  angle  through 
which  the  eye  turns.  But  as  this  angle  is  measured  with  a  large 
radius,  the  result  is  not  vitiated. 

In  accordance  with  their  calculations  we  place  the  center  of 
rotation  at  a  point  on  the  antero-posterior  axis  13.5  mm  behind 
the  anterior  surface  of  the  cornea  in  emmetropia.  In  hyperopia 
the  distance  is  slightly  less,  and  in  myopia  it  is  greater  than  in 
emmetropia. 

Field  of  Fixation. — The  field  of  fixation  measures  the 
rotary  power  of  the  ocular  muscles.  The  maximum  rotation 
which  the  eye  can  make  in  any  direction  is  measured  by  the  angle 
included  between  the  visual  line  in  maximum  rotation  and  the 
visual  line  in  the  primary  position. 

The  average  extent  of  the  field  of  fixation  in  the  normal  eye 
is,  according  to  Landolt,  470  in  all  directions.  Other  authorities 
give  a  higher  degree  of  downward  rotation  and  a  somewhat  less 
degree  of  upward  rotation.  Stevens  assigns  300  as  the  upward 
limit  and  6o°  as  the  downward  limit. 

The  means  which  we  use  for  measuring  the  field  of  fixation 
will  be  given  in  a  subsequent  chapter. 

BINOCULAR  FIXATION 

Binocular  vision  is  the  fusion  into  a  single  perception  of 
the  two  impressions  transmitted  to  the  visual  areas  of  the  brain 
from  the  two  eyes.  There  is  a  slight  dissimilarity  between  the 
two  retinal  images  because  of  the  difference  in  the  position  of 
the  eyes. 

Helmholtz  has  estimated  that  we  can  perceive  a  difference 
in  the  images,  as  seen  monocularly,  for  all  distances  which  do  not 
exceed  240  meters.  In  arriving  at  this  conclusion  he  based  his 
calculations  upon  the  experimental  observation  that  we  can  dis- 
cern a  difference  of  one  minute  of  an  arc. 

By  means  of  this  difference  between  the  images,  and  aided 
by  certain  psychic  influences,  we  are  able  to  estimate  distances 
and  solidity ;  in  other  words,  we  visually  perceive  the  three 
dimensions  of  space  by  the  proper  interpretation  of  the  two  dis- 
similar images  on  our  retinas. 


150  The  Normal  Eye 

The  fusion  of  the  two  images  in  normal  binocular  vision  is 
possible  only  when  the  image  of  direct  vision  falls  upon  the  fovea 
centralis  of  each  eye.  The  visual  lines  must  therefore  meet  at 
the  point  of  fixation.  The  maintenance  of  the  proper  adjustment 
of  the  visual  lines  is  made  poss;ble  by  a  marvelous  correlation  of 
action  of  the  various  ocular  muscles. 

Conjugate  Movements 

When  our  attention  is  directed  to  an  object  which  does  not 
lie  in  the  median  plane  we  may  fix  the  eyes  upon  the  object  either 
by  turning  the  head  or  by  turning  the  eyes  or  by  a  combination 
of  both  movements.  If  we  are  to  gaze  at  the  object  for  any  length 
of  time  we  depend  upon  movement  of  the  head  for  what  we  may 
call  the  coarse  adjustment,  and  upon  movement  of  the  eyes  for  the 
fine  adjustment — for  fixing  the  neighboring  parts  of  the  object. 

When  we  turn  the  two  eyes  so  as  to  fix  an  object  on  our 
right  we  must  call  into  action  the  external  rectus  of  the  right 
eye  together  with  the  internal  rectus  of  the  left  eye.  We  can 
explain  the  simultaneous  contraction  of  these  two  muscles  only 
upon  the  assumption  that  there  exists  in  the  brain  a  connection 
between  the  visual  centers  and  a  certain  center  or  nucleus,  which 
in  turn  is  connected  with  the  external  rectus  of  one  eye  and  with 
the  internal  rectus  of  the  other  eye. 

The  connection  between  the  visual  centers  and  the  muscles 
must,  in  fact,  be  far  more  complicated  than  this  simple  illustra- 
tion would  show.  In  the  various  movements  of  the  eyes  each 
muscle  must  receive  its  appropriate  innervation,  for  although  one 
or  two  of  the  muscles  of  each  eye  may  play  the  more  important 
part,  such  delicate  adjustments  as  are  required  can  only  be 
accomplished  through  the  co-operation  of  all  the  muscles. 

So  intimate  is  the  association  of  the  two  eyes  that  we  cannot 
turn  one  eye  in  any  direction  without  a  corresponding  movement 
of  the  other  eye. 

Listing's  Law. — Torsion  of  the  meridians  would  occur  in 
rotation  of  the  eye  by  a  single  muscle,  other  than  the  internal  or 
external  rectus.  As  the  physiological  movements  of  the  eye  are 
not  produced  by  contraction  of  a  single  muscle,  but  by  a  number 
of  muscles  acting  in  unison,  such  torsion  is  of  interest  chiefly 
in  the  study  of  ocular  paralyses.     We   study  the   physiological 


The  Motor  Mechanism  151 

action  of  the  various  muscles,  and  we  thereby  learn  what  effect 
would  be.  produced  upon  the  rotation  by  the  absence  (from 
paralysis)  of  any  component  element. 

But  torsion  also  occurs  in  the  physiological  oblique  move- 
ments of  the  eye.  This  fact  was  first  shown  by  Donders,  who 
made  the  discovery  by  studying  the  after-images  of  the  eye. 

The  study  of  after-images  was  introduced  by  Ruete.  If,  in  a  darkened 
room,  we  fasten  a  narrow  strip  of  red  ribbon  horizontally  on  a  gray  back- 
ground and  gaze  for  about  a  minute  at  this  ribbon,  upon  turning  the  eye 
to  another  part  of  the  gray  background,  we  shall  see  a  greenish  comple- 
mentary after-image  of  the  ribbon.  For  the  study  of  torsion  we  place 
the  ribbon  on  a  level  with  the  eyes.  After  looking  at  it  for  a  sufficient 
time  we  turn  the  eye  into  an  oblique  position,  as  outward  and  upward. 
The  after-image  of  the  ribbon  will  not  now  be  horizontal ;  it  will  be 
obliquely  inclined  to  the  horizontal  plane.  This  shows  that  the  meridian 
of  the  retina  which  receives  the  image  of  a  horizontal  line  when  the  eye 
is  in  the  primary  position  is  not  the  same  meridian  which  would  receive 
the  image  of  a  horizontal  line  when  the  eye  is  in  the  oblique  position  ;  in 
other  words,  the  retinal  meridians  have  undergone  torsion  with  reference 
to  the  vertical  and  horizontal  meridians. 

The  law  of  torsions  in  its  fullest  sense  was  first  given 
by  Listing.  When  the  eye  turns  from  the  primary  to  any 
secondary  position  it  may  arrive  at  this  secondary  position  either 
by  moving  directly  to  its  new  position,  along  the  shortest  route, 
or  it  may  make  two  or  more  movements  before  arriving  at  the 
final  position.  Listing's  Lazv  simply  states  that  no  matter  how 
the  eye  reaches  the  secondary  position  under  consideration,  the 
torsion  is  the  same  as  if  the  eye  had  turned  directly  from  the 
primary  to  the  secondary  position.* 

Therefore  in  any  secondary  position  which  the  eyes  may 
occupy  we  may  suppose  that  they  have  turned  directly  to  this  posi- 
tion from  the  primary  position.  It  is  apparent  that  in  making 
a  rotation  in  this  manner  the  eye  turns  about  an  axis  which  lies 
in  a  vertical  plane  passing  through  the  centers  of  rotation  of  the 
two  eyes.  This  vertical  transverse  plane  is  called  Listing's  Plane. 
We  do  not  say  that  all  physiological  ocular  rotations  take  place 
around  axes  in  this  plane ;  for  this  is  plainly  not  so  when  the  eye 
turns  from  one  oblique  position  to  another.  But  since  the  posi- 
tion of  the  eye  in  the  last  secondary  position  is  the  same  as  if  it 
had  turned  directly  from  the  primary  position  into  this  secondary 
position,  we  say  that  as  far  as  the  result  is  concerned  all  physio- 


*By  secondary  position  we  meau  any  position  that  is  not  primary. 


152 


The  Normal  Eve 


logical  rotations  may  be  regarded  as  taking  place  around  axes 
lying  in  Listing's  Plane. 

This  applies  to  the  ocular  motions  when  the  eye  is  directed  from  one 
point  of  fixation  to  another.  When  the  head  is  tipped  to  one  side  without 
change  of  the  fixation  point  the  eyes  undergo  a  slight  degree  of  rotation 
around  the  visual  lines  in  their  endeavor  to  maintain  the  meridians  in 
their  usual  relations.  This  is  shown  by  /aval's  experiment  with  cylindrical 
lenses.  If  an  eye  affected  with  astigmia  is  corrected  by  a  lens  the  axis  of 
the  lens  will  not  be  in  the  proper  position  with  regard  to  the  eye  when  the 
head  is  tipped  to  either  side. 

Since  the  change  in  direction  of  the  meridians  which  occurs 
in  conformity  to  Listing's  law  does  not  result   from  an   actual 


hie  76 

Rubber  ball  for  the  study  of 
ocular  rotations 


Fig.  77 

Ophthalmotrope     (Shute). 

For  the  correct  measurement  of  torsion 
the  observer  must  look  along  the  visual  line 
as  represented  by  the  projecting  needle. 
The  outer  metal  ring  represents  Listing's 
plane. 

rotation  around  the  antero-posterior  axis,  it  is  sometimes  called 
false  torsion. 

The  study  of  torsions  is  simplified  by  means  of  models,  called 
ophthalmotropes,   which    represent    the   various    ocular    motions. 
An  inexpensive  device  for  this  study  is  shown  in  Fig.  76.    It  con- 
sists of  a  rubber  ball  painted   so   as  to   show   the  vertical   and 


The  Motor  Mechanism  153 

horizontal  meridians  when  the  eye  is  in  the  primary  position,  and 
mounted  in  the  frame  of  a  hand  magnifying  glass. 

Convergence 

In  binocular  vision  the  conjugate  movements  must  always 
De  associated  with  the  proper  convergence  of  the  visual  lines  so 
that  these  lines  shall  meet  at  the  point  of  fixation. 

Convergence  is  effected  chiefly  by  the  simultaneous  contrac- 
tion of  both  internal  recti,  but  in  conjunction  with  the  appropriate 
contraction  or  relaxation  of  the  other  ocular  muscles.  For  the 
accomplishment  of  this  united  action  there  must  be  a  connection 
between  the  visual  areas  and  a  center — the  convergence  center — 
which  in  turn  must  have  nerve  connections  with  both  internal 
recti,  and  also  secondarily  with  the  nerves  of  the  other  ocular 
muscles. 

The  greater  degrees  of  convergence  are  usually  associated 
with  downward  rotation  of  the  eyes,  as  in  reading.  On  this 
account  convergence  for  a  near  object  is  accomplished  with  much 
less  fatigue  when  the  object  is  below  than  when  it  is  above 
the  eyes. 

In  accordance  with  Listing's  law  there  must  be  positive 
torsion  of  each  eye  when  it  looks  downward  and  inward,  as  in 
convergence  for  a  near  object  below  the  level  of  the 
eyes.  This  fact  has  given  rise  to  much  speculation  as  to 
its  bearing  upon  physiological  vision ;  that  is,  as  to  how  we  are 
able  to  fuse  the  two  images  when  the  meridians  of  the  eye  do 
not  occupy  the  same  relative  position  that  they  do  in  distant 
vision.  Stevens  has  presented  mathematical  evidence  that  the 
torsion  assists  fusion  when  the  object  of  vision  is  in  the  usual 
position  of  a  book  held  for  reading.  Savage,  on  the  other  hand, 
who  would  discard  Listing's  law,  believes  that  there  is  no  torsion, 
but  that  this  is  overcome  by  the  rotary  action  of  the  oblique 
muscles.  The  question  is  too  difficult  and  too  abstruse  to  engage 
our  further  attention,  especially  as  we  must  eventually  acknowl- 
edge that  we  know  almost  nothing  of  the  mental  process  of 
binocular  vision. 

Measurement  of  Convergence. — The  degree  of  con- 
vergence is  measured  by  the  angle  through  which  each  eye  must 
turn  from  parallelism  of  the  visual  lines  so  that  these  lines  may 


154  The  Normal  Eye 

pass  through  the  point  of  fixation.  This  angle  may  be 
measured  in  degrees,  but  we  shall  usually  find  it  more  convenient 
to  express  it  in  terms  of  the  meter-angle. 

A  meter-angle  {ma)  is  that  angle  through  which  each  eye 
must  turn  from  parallelism  of  the  visual  lines  so  that  these 
lines  may  meet  in  the  median  plane  and  at  a  distance  of  one 
meter  from  the  interocular  base  line.  If  the  distance  at  which 
the  visual  lines  meet  is  two  meters  the  convergence  is  expressed 
by  one-half  of  a  meter-angle;  while  if  the  distance  is  one-half 
of  a  meter  the  convergence  is  two  meter-angles,  and  so  on. 

This  system  has  the  advantage  that  in  emmetropia  the  con- 
vergence, as  expressed  in  meter-angles,  is  equal  to  the  accommo- 
dation as  expressed  in  diopters. 

The  chief  objection  to  this  unit  is  that  it  has  no  fixed  value, 
since  the  value  varies  with  the  interocular  distance.  This  distance 
ranges  from  50  mm  to  75  mm,  and  by  calculation  we  find  that 
within  these  limits  the  meter-angle  varies  between  1.40  and  2.1  °. 

The  average  interocular  distance  in  the  adult  is  given  as 
64  mm,  which  gives  1.830  as  the  average  value  of  the  meter-angle. 
This  corresponds  approximately  to  the  deviation  produced  by  a 
prism  of  3^  A.  Therefore  if  we  use  this  average  as  a  standard, 
one  meter-angle  of  convergence  is  equivalent  to  the  effect  of  a 
prism  of  3^2  a,  base  out,  before  each  eye,  or  to  the  effect  of  a 
prism  of  7  a   before  one  eye. 

Near  Point  of  Convergence. — By  the  near  point  of  con- 
vergence we  mean  the  nearest  point  for  which  the  eyes  can 
converge.  Landolt  estimates  that,  as  an  average,  this  point  lies 
-1  of  a  meter  (10.5  cm  or  about  4  inches)  from  the  interocular 
base  line.     This  represents  a  converging  potver  of  9.5  ma. 

Relaxation     of     Convergence. — Although     the     simpl 


e 


relaxation  of  the  internal  recti  will  diminish  the  convergence, 
the  full  relaxation  can  only  be  accomplished  by  the  simultaneous 
contraction  of  the  external  recti.  This  implies  that  there  must 
be  a  nerve  center  for  divergence  as  well  as  for  convergence, 
and  that  these  two  centers  must  be  in  intimate  association. 

Far  Point  of  Convergence. — In  the  human  race,  possessed 
of  binocular  vision,  absolute  divergence  of  the  visual  lines  does 
not  exist  as  a  normal  condition.  In  distant  vision  there  is  no 
convergence — the  convergence    point   is    at    an    infinite    distance. 


The  Motor  Mechanism  155 

We  might  suppose,  therefore,  that  parallelism  of  the  visual  lines 
would  represent  the  maximum  relaxation  of  convergence ;  but  it 
is  not  so,  for  by  the  interposition  of  a  prism  we  can  show  that 
normal  eyes  are  capable  of  an  actual  divergence. 

Divergence  of  the  visual  axes  is  expressed  as  negative  con- 
vergence. The  negative  range  of  convergence  is  normally  about 
one  meter-angle.  This  corresponds  to  a  prism  of  3*^2  a  placed 
before  each  eye,  with  its  base  towards  the  nose. 

Association  of  Accommodation  and  Convergence. — In 
normal  vision  every  change  in  convergence  is  accompanied  by 
a  corresponding  change  in  accommodative  impulse.  In 
emmetropia  vision  at  one  meter  is  accomplished  with  1  D  of 
accommodation  and  1  ma  of  convergence ;  at  one-third  of  a  meter 
there  must  be  exercised  3  D  of  accommodation  and  3  ma  of 
convergence,  and  so  on.  So  intimate  is  the  association  between 
these  two  functions  that  exercise  of  one  of  them  is  involuntarily 
accompanied  by  a  corresponding  action  of  the  other. 

Although  normally  associated,  accommodation  and  con- 
vergence are  not  indissolubly  connected.  With  exercise  of  a  fixed 
degree  of  convergence  the  amount  of  accommodation  may,  within 
certain  limits,  be  varied,  and  vice  versa. 

If  a  weak  concave  lens  is  placed  before  each  eye  of  an 
emmetrope.  he  can  still  see  a  distant  object  clearly  by  exercise  of 
accommodation  while  the  visual  axes  remain  parallel ;  but  when 
the  strength  of  the  concave  lenses  is  increased  beyond  a  certain 
limit,  either  the  object  will  appear  indistinct  from  insufficient 
accommodation  or  diplopia  will  result  from  convergence  of  the 
visual  lines.  The  limit  of  accommodation  with  parallelism  of  the 
visual  lines  is  slightly  more  than  3  D  ( Ponders)  for  an 
emmetrope  fifteen  years  of  age. 

The  addition  of  a  convex  lens  to  each  eye  in  emmetropia 
would  render  a  distant  object  indistinct,  since  no  further  relaxa- 
tion of  accommodation  is  possible;  but  if  a  near  object  is  viewed, 
the  accommodation  may,  within  certain  limits,  be  increased  by 
concave  lenses  and  diminished  by  convex  lenses,  while  the  con- 
vergence remains  unchanged.  In  vision  at  33  on,  the  requisite 
convergence  being  3  ma,  accommodation  may  be  varied  from  .5  D 
(by  convex  lenses)  to  6.5  D  (by  concave  lenses)  in  an  emmetrope 
fifteen  years  of  age    (Donders). 

The  difference  between  the  least  and  the  greatest  amount  of 


156 


The  Normal  Eye 


accommodation  that  is  possible  with  a  fixed  convergence  consti- 
tutes the  relative  range  of  accommodation. 

Donders  determined   the   relative   range   of   accommodation 
in  various   individuals  with   different  refractive  conditions,   and 


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FIG.    78 
Accommodation    and   convergence    (Donders). 

expressed  his  results  in  what  is  called  the  graphic  method.  This 
method  is  illustrated  in  Fig.  78,  which  is  Donders' s  diagram  of 
the  relative  range  of  accommodation  in  an  emmetrope  of  fifteen 
years  of  age. 

In  the  chart  the  diagonal  line  represents  the  convergence; 
Pi  P2  P  represents  the  maximum  of  accommodation  possible  with  a 
given  convergence ;  and  r  r1  rx  represents  the  minimum  of  accom- 
modation. The  accommodation  in  diopters  is  read  from  the 
vertical  column  of  figures,  and  the  convergence  in  meter-angles 
is  read  from  the  horizontal  markings. 

Hess  has  more  recently  made  studies  of  the  relative  accom- 
modation, and  by  more  exact  means  than  were  used  by  Donders 
has  obtained  a  somewhat  different  result.  His  chart  is  shown  in 
Fig"-  79-  We  see  that  the  accommodation  lines  are  parallel  to  the 
convergence  line. 


The  Motor  Mechanism 


157 


As  the  accommodation  can  be  varied  while  convergence  is 
unaltered,  so  the  convergence  may,  within  certain  limits,  be 
increased  or  diminished  without  change  of  accommodation.  This 
has  already  been  shown  in  connection  with  the  diverging  power 
of  the  eyes.  By  means  of  prisms  (bases  in)  a  divergence  of  1 
ma  may  be  made  when  the  accommodation  is  completely  relaxed. 
By  means  of  prisms  also  (bases  out)  a  convergence  of  about  2  ma 
may  be  made  without  exercise  of  accommodation.  With  3  D 
of  accommodation  convergence  may  vary  from  zero  (parallelism) 
to  about  6  ma.  The  difference  between  the  least  and  greatest 
convergence  with  a  fixed  amount  of  accommodation  represents 
the  relative  range  of  convergence. 

The  diagram  which  gives  the  relative  range  of  accommo- 
dation  may   also   be   used   to   show   the   relative   range   of  con- 


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fig.  79 

Accommodation   and   convergence    (Hess). 


vergence;  for  the  horizontal  scale  records  the  greatest  and  least 
convergence  which  is  possible  with  a  fixed  amount  of  accommo- 
dation. 

This  latitude  in  the  relative  accommodation  and  con- 
vergence is  of  great  importance,  for  it  is  through  this  variation 
that  comfortable  binocular  vision  is  frequently  possible  in 
ametropia,  and  that  the  accustomed  relation  in  ametropia  may  be 
disturbed  by  correcting  lenses  with  at  least  only  temporary 
discomfort. 


158  The  Normal  Eye 

Accommodation   and   Convergence   in   Side   Vision. — 

The  relation  between  accommodation  and  convergence  under- 
goes a  change  when  we  move  our  eyes  from  an  object  in  the 
median  plane  to  either  side  of  this  plane.  Further,  the  question 
arises  as  to  the  manner  of  accommodation  in  such  vision ;  that  is, 
whether  a  greater  amount  of  accommodation  is  used  with  one  eye 
than  with  the  other,  or  whether  vision  is  blurred  in  both  eyes,  or 
whether  one  eye  accommodates  properly  for  the  object  while  the 
other,  exercising  the  same  degree  of  accommodation,  receives  a 
blurred  image.  It  is  generally  thought  that  the  last  is 
Nature's  method,  and  that  the  eye  which  is  farther  from  the 
object,  requiring  the  less  accommodation,  adapts  itself  for  the 
object.  We  do  not,  however,  ordinarily  look  intently  at  objects 
much  removed  from  the  median  plane,  for  when  an  object  so 
situated  attracts  our  attention,  we  turn  our  head  towards  the 
object. 

CORRESPONDING  POINTS 

The    Horopter 

We  have  learned  that  in  binocular  vision  the  image  of  the 
point  of  fixation  falls  upon  the  center  of  the  fovea  of  each  eye. 
If  from  any  cause  the  image  of  fixation  falls  upon  the  fovea  of 
one  eye  and  upon  some  other  part  of  the  retina  of  the  other  eye, 
double  z'ision  results.  The  centers  of  the  two  foveas  are 
corresponding  points  of  the  two  retinas,  but  any  other  part  of 
the  retina  of  one  eye  is  a  disparite  point  with  reference  to  the 
fovea  of  the  other  eye.  Owing  to  the  nerve  relationship  between 
the  retinas  and  the  visual  centers,  we  cannot  form  a  single  impres- 
sion from  the  two  images  as  formed  upon  disparite  points  of 
the  retinas. 

A  great  amount  of  labor  was  expended  by  Helmholts  and 
others  in  the  study  of  the.  horopter.  By  this  term  we  mean 
the  surface  containing  all  the  points  which  would  be  seen  singly 
for  any  fixed  adjustment  of  the  eyes;  that  is,  the  horopter  con- 
tains all  the  points  whose  images  would  fall  upon  corresponding 
points  of  the  two  retinas. 

In  any  given  adjustment  of  the  eyes  there  would  always  be 
a  large  part  of  the  field  of  vision  in  which  objects  would  not  fall 
upon  corresponding  points :  but  as  we  do  not  ordinarily  see  such 
outlying  objects  double,  it  is  of  no  importance  that  they  do  not 


The  Motor  Mechanism  159 

lie  in  the  horopter.  Furthermore,  we  are  not  warranted  in  assum- 
ing that  corresponding  geometrical  points  are  so  correlated  with 
the  visual  centers  that  these  same  points  correspond  in  a  physio- 
logical sense.  In  fact,  if  we  should  thus  determine  the 
corresponding  points  with  the  eyes  in  the  primary  position,  the 
same  points  would  not  correspond  with  the  eyes  in  convergence. 

Why  then  do  we  not  see  doubled  the  objects  which  do  not 
lie  in  the  horopter?  The  answer  is  that  vision  is  a  process  of  the 
mind.  The  human  race  has  acquired  the  faculty  of  binocular 
vision.  We  have  learned  to  fuse  the  two  images  of  direct  vision, 
but  we  devote  only  slight  attention  to  the  objects  of  indirect 
vision,  and  if  a  double  impression  is  made  on  the  visual  areas,  it 
is  not  conveyed  to  the  centers  of  consciousness.  By  properly 
directing  our  attention  we  can  experimentally  elicit  double  vision 
under  certain  circumstances  when  we  should  not  ordinarily  be 
aware  that  it  existed. 

NORMAL  MUSCULAR  EQUILIBRIUM 

In  a  state  of  complete  repose  the  directions  of  the  visual 
lines  are  determined  by  the  relative  lengths  of  the  extra-ocular 
muscles  when  these  are  all  in  complete  relaxation.  Entire  absence 
of  innervation  of  these  muscles  exists,  however,  only  during  , 
closure  of  the  lids,  in  sleep  (natural  or  narcotic)  and  in  blindness. 
Examinations  show  that  under  these  conditions  the  eyes  usually 
assume  more  or  less  divergence  in  accordance  with  the  divergence 
of  the  orbits,  which  would  give  in  man,  as  in  the  lower  animals, 
a  natural  divergence  of  the  eyes,  if  this  tendency  were  not  over- 
come, by  the  capacity  for  binocular  single  vision. 

But  since  complete  muscular  relaxation  does  not  occur  in 
physiological  vision,  the  effect  of  such  relaxation  upon  the  direc- 
tions of  the  visual  lines  is  of  minor  importance.  The 
question  is,  What  is  the  position  of  equilibrium  of  the  ocular 
muscles  during  vision?  In  distant  emmetropic  vision  no  accom- 
modation is  required  and  the  visual  lines  are  parallel ;  convergence 
must  be  exactly  neutralized  by  the  external  recti,  and  the  vertical 
adjustment  must  exactly  correspond  in  the  two  eyes.  If  the 
relation  between  accommodation  and  the  extra-ocular  muscles  is 
perfectly  adjusted,  the  eyes  will  assume  the  proper  position  for 
binocular  single  vision,  even  though  one  eye  may  be  excluded 


160  The  Normal  Eye 

from  vision.     This  is  the  ideal   (normal)  muscular  equilibrium* 
it  is  called  orthophoria. 

On  the  other  hand,  binocular  single  vision  may  be  habitually 
performed,  either  with  or  without  discomfort,  and  yet  when  one 
eye  is  excluded  from  vision  it  will  involuntarily  move  inward 
(esophoria)  or  outward  (exophoria),  or  upward  or  downward 
(right  or  left  hyperphoria).  Any  such  deviation  from  orthophoria, 
is  called  heterophoria. 

The  following'  authorities  have  been  consulted  in  the  prepara- 
tion of  the  foregoing-  chapter: 

Tenon,  Memoires  et  a" observations  sur  f  anatomie. 

Bonnet,  Des  Aponeuroses  ct  des  Muscles  des  I'oeil,  Traite  de 
Sect.  tend,  et  muscl. 

Motais,  Anatomie  de  I'apparcil  moteur  de  I'oeil. 

Maddox,  Ocular  Muscles. 

Stevens,  Motor  Apparatus  of  the  Eyes. 

Savage,  Ophthalmic  Myology,  and  Ophthalmic  Neuro- 
Myology. 

Donders,  Anomalies  of  Refraction  and  Accommodation. 

Landolt,  Refraction  and  Accommodation;  and  Anomalies  of 
the  Motor  Apparatus  of  the  Eyes,  Norris  and  Oliver's  System 
of  Diseases  of  the  Eye. 

Duane,  The  Extra-Ocular  Muscles,  Posey  and  Spiller's,  Eye 
and  Nervous  System. 

Helmholtz,  Optique  Physiologique. 

Ruete  (Listing's  Lazv),  Lehrbuch  der  Ophthalmologic 

Fuchs,  Text-Book  of  Ophthalmology,  and  Beitrdge  zur  nor- 
malen  Anatomie  des  Augapfels,  Arch,  fur  Ophthal.,  1894. 

Hess,  Refraction  and  Accommodation,  Graefe-Saemisch 
Handbuch,  2nd.  ed. 

Koster,  Die  Accom.  und  Conv.  bei  seitlicher  Blickrichtung 
Arch  fur  Ophthal.,  1896. 

Shute,  Torsion  of  the  Eyeball,  N.  Y.  Med.  Jour.,  1910. 

Tscherning,  Physiologic  Optics. 

Javal,  Anom.  de  I'accom.  et  de  la  Refr.  (Donders),  de 
Wecker's  Traite  des  Mai.  des  Yeux. 


PART   III 

ERRORS  OF  REFRACTION 


CHAPTER  X 

OPTOMETRY  OF  THE  REFRACTIVE  APPARATUS 

The  various  methods  which  are  at  our  command  for  deter- 
mining the  refractive  condition  of  the  eye  may  be  divided  into 
two  general  classes:  (i)  subjective  methods,  and  (2)  objective 
methods.  In  the  former  method  the  examiner  is  guided  by  the 
statements  of  the  person  undergoing  examination,  while  in  the 
latter  he  relies  solely  upon  his  own  judgment. 

Subjective  Methods 

Optometers  Based  upon  the  Action  of  a  Convex  Lens. 

— A  single  convex  spherical  lens  placed  before  the  eye  constitutes 
the  simplest  of  optometers. 

We  know  that  if  the  distance  from  the  lens  to  an  object  is 
greater  than  the  focal  length  of  the  lens,  rays  from  the  object 
will  enter  the  eye  in  convergent  pencils,  and,  consequently,  will 
be  focused  on  the  retina  only  when  the  eye  is  hyperopic.  If  the 
distance  from  the  lens  to  the  object  is  equal  to  the  focal  length 
of  the  lens,  the  rays  from  any  point  of  the  object  will  be  parallel 
when  they  enter  the  eye,  and  will  be  focused  on  the  retina  of  an 
emmetropic  eye.  Finally,  if  the  distance  between  the  object  and 
the  lens  is  less  than  the  focal  length  of  the  lens,  rays  from  any 
point  of  the  object  will  enter  the  eye  in  divergent  pencils,  and  can 
be  focused  on  the  retina  only  when  the  eye  is  myopic  or  exercising 
accommodation.  If,  therefore,  the  object  is  so  small  that  it  can- 
not be  distinguished  unless  its  image  is  accurately  formed  on  the 
retina,  we  can  judge  by  the  position  of  the  lens  whether  an  eye  is 
hyperopic,  emmetropic,  or  myopic. 

Optometers  of  this  kind  have  two  disadvantages :   ( 1 )  The 

161 


1 62 


Errors  of  Refraction 


magnifying  power  is  variable;  and  (2)  the  nearness  of  the  test 
•object  provokes  an  accommodative  impulse,  by  which  the  result 
of  the  examination  is  rendered  uncertain. 

Optometers  Based  upon  the  Principle  of  the  Opera 
Glass  or  Galileo's  Telescope. — Optometers  of  this  kind  consist 
of  a  combination  of  a  strong  concave  lens,  or  eye-piece,  with  a 
weaker  convex  lens,  or  objective.  By  varying  the  distance  be- 
tween the  two  lenses  different  refractive  effects  are  produced.  If 
the  two  lenses  are  in  contact,  the  effect  of  the  concave  lens,  which 
is  the  stronger,  predominates,  and  the  combination  is  equivalent 
to  a  concave  lens  whose  strength  is  equal  to  the  difference  in 
power  between  the  two  lenses ;  but  as  the  convex  lens  is  with- 
drawn from  the  eye  its  refractive  effect  in  distant  vision  increases, 
and  in  a  certain  position  the  two  lenses  exactly  neutralize  each 
other.  By  further  withdrawal  of  the  convex  lens  the  combina- 
tion finally  becomes  equal  to  a  convex  lens. 

According  as  a  distant  object  appears  distinct  to  the  eye 
under  examination  when  the  foregoing  combination  has  a 
convex,  a  plane,  or  a  concave  effect,  the  eye  is  hyperopic, 
emmetropic  or  myopic,  and  from  a  suitably  constructed  scale  the 
degree  of  ametropia  can  be  determined.  But  this  test  also  lacks 
accuracy  because  the  magnifying  power  of  the  convex  lens  in- 
creases as  it  is  withdrawn  from  the  eye. 

Optometers  Based  upon  Scheiner's  Experiment. — 
When  one  looks  through  minute  openings  at  a  small  object 
placed  at  a  distance  for  which  the  eye  is  not  adapted,  the  object 


fig.  80 

Scheiner's  Experiment 


appears  multiplied,  for  each  opening  furnishes  a  separate  image. 
This  phenomenon,  called  Scheiner's  experiment,  is  illustrated 
in  Fig.  80.  Let  O  represent  a  point  of  light,  D  D  the  dia- 
phragm, and  A  and  B  two  openings  in  the  diaphragm.  If  /  is  con- 
jugate to  O.  and  if  the  retina  intersects  the  axis  at  /,  there  will 


Optometry   of   the  Refractive  Apparatus  163 

be  a  single  image  of  the  point  O.  If  the  retina  lies  in  front  of  /, 
the  light  passing  through  the  opening  A  will  fall  upon  the  retina 
at  a  and  that  passing  through  B  will  fall  upon  b,  and  since  an 
image  on  the  retina  above  the  axis  corresponds  to  an  external 
object  below,  and  vice  versa,  it  is  apparent  that  the  image  which 
is  formed  by  the  light  passing  through  the  upper  diaphragm 
appears  below  while  the  image  formed  by  the  light  passing  through 
the  lower  diaphragm  appears  to  be  above  the  axis.  In  other 
words  the  two  images  are  inverted  with  respect  to  the  openings 
in  the  diaphragm. 

If,  on  the  other  hand,  the  retina  lies  behind  /,  the  image  a' 
will  be  below  and  b'  will  be  above,  and  in  projecting  these  images 
externally  through  the  nodal  point  of  the  eye  the  relative  position 
of  the  two  lights  will  be  the  same  as  the  openings  in  the  diaphragm. 

We  may  therefore  use  this  phenomenon  to  determine  the 
refractive  condition  of  the  eye.  We  place  a  red  glass  before  one 
of  the  openings  so  as  to  distinguish  the  two  images.  The  point 
of  light  is  furnished  by  a  small  flame  or  electric  light  six  meters 
distant  from  the  eye.  When  a  single  image  is  seen  the  eye  is 
emmetropic.  When  two  images  are  seen,  the  relative  position 
being  opposite  to  that  of  the  openings  in  the  diaphragm,  the  eye 
is  hyperopic.  When  the  relative  position  is  the  same  as  that  of  the 
two  openings  the  eye  is  myopic.  By  placing  the  proper  lens  before 
the  eye  the  two  images  may  be  united  and  the  degree  of  ametropia 
measured  thereby. 

The  optometer  of  Thomas  Young,  which  Tscherning  has 
found  valuable  in  the  study  of  accommodation,  is  based  upon 
the  principle  of  Scheiner.  The  method  of  producing  the  multiple 
images  with  this  optometer  is  shown  in  Fig.  81.  If  we  hold  the 
diaphragm  before  the  eye  so  that  two  or  more  of  the  slits  come 
within  the  pupillary  area  while  we  look  at  a  straight  line,  whose 
length  lies  in  the  line  of  vision,  we  see  a  separate  line  for  each' 
slit,  and  these  lines  converge  to  the  point  which  is  conjugate  to  the 
retina.  (Fig.  81.)*  While  this  optometer  is  of  great  scientific 
interest  it  is  not  suitable  for  the  practical  determination  of  the 
refractive  condition. 

Optometers    Based    upon    Chromatic    Aberration. — 
In  the  application  of  this  property  the  examinee  looks  at  a  small 


*On    account    of    the    spherical    aberration    of    the    eye    the    lines    do    not    actually 
meet  in  a  common  point. 


164 


Errors  of  Refraction 


round  area  of  light  five  or  six  meters  distant.  The  eye  is  covered 
with  cobalt  blue  (purple)  glass,  which  allows  both  blue  and  red 
light  to  pass  through  it.  The  blue  rays,  being  more  strongly  re- 
fracted than  the  red  rays,  are  brought  to  a  focus  sooner  than  the 
red.  If  the  blue  rays  are  focused  slightly  in  front  of  the  retina 
and  the  red  rays  slightly  behind  it,  the  image  of  a  point  of  light 


a 


(a). — Diaphragm    of    Young's    optometer. 

(£>). — Appearance   of  a  line  as  seen  with  Young's  optometer. 

will  be  a  small  diffusion  circle,  in  which  both  red  and  blue  light 
will  be  present,  and  the  point  will  be  seen  as  a  small  purple  spot. 
This  is  the  condition  in  emmetropia.  If  the  eye  is  hyperopic, 
the  blue  rays  will  be  more  nearly  focused  than  the  red  rays. 
Hence,  there  will  be  formed  on  the  retina  a  diffusion  circle,  the 
central  part  of  which  will  contain  both  blue  and  red  rays,  but  more 
blue  than  red,  and  the  outer  part  will  contain  only  red  rays.  The 
image  will,  therefore,  appear  as  a  central  blue  area  surrounded  by 
a  red  band.  On  the  other  hand,  in  myopia,  both  red  and  blue  rays 
having  passed  their  foci  before  reaching  the  retina,  the  blue  will  be 
more  diffused  than  the  red  light.  Hence,  the  central  part  of  the 
diffusion  circle  will  contain  mostly  red  and  the  outer  part  only 
blue  light.  The  image  will,  therefore,  appear  as  a  central  area  of 
red  surrounded  by  a  band  of  blue  light. 

The  degree  of  ametropia  may  be  ascertained  by  placing  before 
the  eye  such  a  lens  as  will  render  the  image  uniformly  purple 
throughout.    This  lens  is  the  measure  of  the  ametropia. 

Optometers  Based  upon  the  Measurement  of  the 
Retinal     Diffusion     Circles. — Two    distant    points    of    light 


Optometry   of   the  Refractive  Apparatus  165 

separated  by  a  sufficient  interval  will  appear  separate  and  distinct 
to  the  emmetrope;  but  to  the  ametrope  the  points  will  appear  as 
two  bright  disks  whose  size  will  increase  with  the  degree  of 
ametropia.  If  the  diffusion  circles  are  sufficiently  large,  these 
disks  will  appear  to  overlap,  and  the  distance  between  the  two 
lights  must  be  increased  in  order  that  the  images  may  be  entirely 
separated.  From  a  suitably  constructed  scale  the  degree  of 
ametropia  may  be  estimated  by  observing  the  least  distance  which 
may  intervene  between  the  two  lights  while  they  are  seen  as 
separate.     Thomson's  ainetrometcr  is  based  upon  this  principle. 

Optometry  Based  upon  Movement  of  the  Diffusion 
Image  on  the  Retina. — If  one  looks  at  a  distant  point  of 
light  through  a  stenopeic  slit  which  is  moved  from  side  to  side, 
he  sees  an  apparent  movement  of  the  light  except  when  his  eye 
is  so  adapted  as  to  focus  the  light  on  his  retina.  This  is  apparent 
from  Fig.  80,  which  was  used  in  illustration  of  Scheiner's  experi- 
ment. We  may  assume  that  A  represents  the  first  position  of  the 
stenopeic  opening  and  B  the  position  into  which  it  is  subsequently 
moved.  If  the  eye  is  hyperopic,  the  retinal  image  of  O  will  fall 
at  a  in  the  first  position,  and  as  the  slit  is  moved  to  B  the  image 
will  move  to  b.  If  the  eye  is  adapted  for  the  point  0,  the  image 
remains  at  /  in  all  positions  of  the  slit.  If  the  eye  is  myopic,  the 
image  moves  from  a  to  b'  when  the  slit  moves  from  A  to  B. 
Hence,  if  O  is  a  distant  point  of  light  the  eye  is  hyperopic  or 
myopic  according  as  movement  of  the  slit  causes  an  opposite  or  a 
like  displacement  of  the  light.  The  lens  which  neutralizes  the 
displacement  measures  the  ametropia.  This  test,  under  the  name 
of  kinescopy,  has  been  advocated  by  Holth. 

Optometry  Based  upon  Visual  Acuteness. — The 
foregoing  methods  of  optometry  are  of  scientific  interest,  and 
some  of  them  are  occasionally  used  in  practical  work,  but  for 
general  use  the  one  subjective  method  which  is  indispensable 
consists  in  testing  the  visual  acuteness  with  trial  lenses. 

Visual  acuteness  is  measured  by  the  least  interval  which  may 
exist  between  two  points  while  they  are  still  distinguished  as 
separate.  It  is  apparent  that  this  interval,  as  measured  on  the 
retina,  cannot  be  less  than  the  diameter  of  one  sentient  element 
of  this  organ ;  for  when  two  adjacent  elements  are  illuminated  no 
interval   of   darkness   can   exist   between   the   two  points. 

The  interval  between  retinal  cones  in  the  macular  region  is 


1 66 


Errors  of  Refraction 


probably  about  0.002  mm,  and  this  length  subtends,  at  the  nodal 
point  of  the  eye  an  angle  somewhat  less  than  one-half  of  a  minute. 
Since  an  object  subtends  at  the  nodal  point  the  same  angle  which 
the  image  subtends  at  this  point,  we  should  suppose  that 
the  minimum  visual  angle  for  distinguishing  points  would  be 
about  one-half  of  a  minute;  but,  because  of  the  imperfections 
of  the  eye,  we  find  that,  even  under  favorable  circumstances,  it  is 
rarely  possible  for  us  to  distinguish  points  separated  by  so  small 
an  interval. 


fig.  82 

Test  letter  con- 
structed according  to 
Snellen's   principle. 


FIG.    84 

Landolt's   Chart 


E 

R   H     * 

■    Z  D  V    " 

•  T  H  L  E    * 

•  A   R   N   P   H    - 

•  c  n  k   T  e  0  - 

FIG.    83 
Test   Card 

The  astronomer  Hooke,  in  1674,  made  the  first  investigations 
to  ascertain  the  minimum  visual  angle.  Taking  the  multiple  stars 
as  the  points,  he  found  that  in  no  case  could  any  interval  be  dis- 
tinguished when  the  angle  was  less  than  one-half  of  a  minute, 
and  in  most  cases  an  angle  of  one  minute  was  required  in  order 
that  the  interval  could  be  distinguished. 

For  practical  purposes  a  series  of  parallel  lines,  also  used 
by  Hooke,  affords  a  more  convenient  means  of  testing  visual 
acuteness.  The  least  angle  which,  under  favorable  circumstances, 
may  separate  black  lines  on  a  white  ground  while  the  interval 
between  them  is  perceived  is  about  fifty  seconds  (50").  This 
angle  corresponds  to  a  linear  distance  on  the  retina  of  slightly 
more  than  0.004  wtm;  that  is,  it  is  more  than  twice  the  diameter 
of  one  retinal  cone. 

In  accordance  with  these  facts,  Snellen,  in  1862,  constructed 
a  series  of  test-letters,  which  he  called  optotypes,  for  the  examina- 
tion of  visual  acuteness.    The  whole  letter  in  each  case  subtends 


Optometry   of   the  Refractive  Apparatus  167 

an  angle  of  five  minutes  when  in  the  proper  position,  and  each 
stroke  of  the  letter  subtends  an  angle  of  one  minute  (Fig.  82). 

Since  many  eyes  do  not  have  the  normal  visual  acuteness, 
we  have  letters  of  different  sizes,  the  distance  at  which  the  letters 
subtend  an  angle  of  five  minutes  being  denoted  for  the  letters  of 
each  separate  size  (Fig.  83). 

In  order  to  facilitate  relaxation  of  the  accommodation  we 
place  the  letters  at  a  distance  of  five  or,  preferably,  six  meters 
from  the  eye  undergoing  examination. 

If  the  distance  is  six  meters  and  if  the  examinee  can  read 
those  letters  which  subtend  a  visual  angle  of  five  minutes,  the 
eye  possesses  normal  visual  acuity.  This  is  recorded  thus : 
V  =  6/6  or  V  =  1.  But  if  at  this  distance  the  examinee  can  read 
no  smaller  letters  than  those  which  should  be  read  at  nine  meters, 
the  visual  acuteness  is  recorded  by  the  expression  V  =  6/9.*  The 
distance  at  which  the  examination  is  conducted  is  the  numerator, 
and  the  distance  at  which  the  smallest  distinguishable  letters 
should  be  read  is  the  denominator  of  the  fraction  expressing  the 
visual  acuteness. 

We  have  seen  that  the  minimum  visual  angle  is  somewhat 
smaller  than  the  angle  required  for  normal  (V  =  6/6)  vision  as 
indicated  by  Snellen's  test-letters;  moreover,  it  is  not  necessary 
for  one  to  see  distinctly  all  the  lines  of  a  letter  with  which  he  is 
familiar  in  order  to  read  the  letters  correctly.  It  not  infrequently 
happens,  therefore,  that  one  can  read  at  a  distance  of  six  meters 
the  letters  which  subtend  the  five-minute  angle  at  four  meters,  or 
even  at  three  meters,  and  we  may  thus  have  V  =:  6/4  or  V  =  6/3. 
It  is,  in  fact,  the  rule  in  young  persons  for  the  visual  acuteness  to 
exceed  the  normal  as  indicated  by  the  test-letters.  After  middle 
age  the  visual  power  undergoes  a  diminution  and  vision  exceeding 
6/6  does  not  so  often  occur. 

Because  visual  acuteness  so  frequently  surpasses  the  standard 
fixed  by  Snellen,  his  plan  has  been  modified  by  the  substitution 
of  a  four-minute  angle.  Nothing  is  gained  by  this  substitution 
of  a  standard,  which,  while  more  accurate  for  the  young,  is  too 
high  for  middle  and  old  age.  The  average  normal  visual  acuteness 
is  sufficiently  approximated  by  Snellen's  five-minute-angle  stand- 

*The  method  sometimes  adopted  of  expressing  the  visual  acuteness  as  a  decimal 
fraction  has  the  disadvantage  of  not  indicating  the  distance  at  which  the  test  has 
been  made. 


168  Errors  of  Refraction 

ard,  and  any  alteration,  unless  universally  adopted,  can  only  lead 
to  confusion. 

Of  the  other  modifications  of  Snellen's  system,  it  suffices  to 
mention  that  of  Landolt,  who  has  substituted  for  the  alphabetical 
characters  a  circle  having  an  opening  in  its  circumference  (Fig. 
84).  The  size  of  the  hiatus  conforms  to  the  minimum  visual 
angle  of  Snellen.  The  character  is  varied  by  placing  the 
hiatus  in  different  positions.  This  plan  has  a  number  of  advan- 
tages from  a  scientific  point  of  view  over  the  use  of  letters ; 
yet,  because  of  the  convenience  of  the  latter,  it  is  probable  that 
they  will  continue  in  common  use.  Landolfs  charts  are,  however, 
especially  convenient  for  illiterates. 

Since  some  persons  very  soon  memorize  the  test-letters,  it  is 
well  to  have  a  number  of  test-cards,  and  in  the  selection  of  these 
it  is  important  that  we  have  all  the  cards  uniform  in  respect  to 
the  size  and  distinctness  of  the  letters  which  are  to  be  read  at  the 
specified  distance. 

In  making  use  of  this  method  of  examination  care  must  be 
taken  to  provide  suitable  illumination.  If  sufficient  daylight  is  not 
available,  gas  or  electric  light  may  be  used,  proper  shades  being 
employed  in  order  that  the  direct  rays  from  the  lamp  will  not  reach 
the  eyes. 

Each  eye  should  be  tested  separately  and  the  eye  not  under- 
going examination  should  be  excluded  by  an  opaque  disk. 

When  it  is  desired  merely  to  test  the  visual  power  without 
the  aid  of  lenses,  all  that  is  necessary  is  to  place  the  individual 
and  test-card  in  proper  position  and  to  observe  the  smallest  letters 
which  he  can  read.  The  distance  at  which  the  letters  are  read 
divided  by  the  distance  at  which  they  ought  to  be  read  expresses 
the  visual  power. 

But  when  our  object  is  to  discover  the  refractive  condition 
of  the  eye,  we  must  select  and  place  before  the  eye  that  lens 
which  produces  the  highest  obtainable  degree  of  vision. 
Furthermore,  since  we  wish  to  compare  the  visual  acuity  with  that 
of  a  normal  emmetropic  eye,  we  must  endeavor  so  to  place  the 
lens  that  the  retinal  images  will  be  of  the  same  size  as  that  of  the 
emmetropic  eye. 

The  lens  which,  when  placed  in  proper  position  (15  mm 
from  the  eye),  affords  the  maximum  visual  power  measures  the 


Optometry   of   the  Refractive   Apparatus  169 

ametropia,  for  it  is  evident  that  the  highest  power  of  vision  will 
be  obtained  when  the  image  is  accurately  focused  on  the  retina. 

Trial  Lenses.— In  order  to  facilitate  the  selection  of  the 
proper  lens,  the  examiner  must  provide  himself  with  a  case  of 
trial  lenses.  This  consists  of  pairs  of  convex  and  concave  spherical 
and  cylindrical  lenses,  prisms,  plane  and  colored  glasses,  opaque 
disks,  stenopeic  disks,  trial  frames  for  holding  the  lenses  before 
the  eye,  and  other  accessories. 

In  the  complete  case  the  interval  between  lenses  is  0.125  D 
for  those  below  2  D  in  strength ;  0.25  D  for  those  between  2  D 
and  5  D;  0.50  D  for  those  between  5  D  and  8  D;  and  1  D  for 
those  between  8  D  and  2$  D,  the  last  named  being  the  highest 
power  usually  furnished  in  the  case,  and  this  only  in  the  spherical 
lenses.  The  cylindrical  lenses  ordinarily  do  not  exceed  6  D  or 
8  D  in  strength,  though  more  elaborate  cases  are  made  in  which 
these  lenses  are  supplied  up  to  16  D. 

The  dioptric  power  is  marked  on  each  lens,  the  plus  (  +  ) 
sign  being  used  to  denote  convex,  and  the  minus  ( — )  sign  to 
denote  concave  lenses.  In  the  cylindrical  lenses  the  position' of  the 
axis  is  marked  on  the  glass,  and,  in  order  that  this  position  may 
be  determined  at  a  glance,  the  peripheral  part  of  the  lens  is  usually 
rough-ground  in  a  direction  parallel  to  the  axis. 

Determination  of  the  Power  and  Center  of  a  Lens. — 
It  is  obviously  necessary  that  we  should  be  able  to  determine 
quickly  the  kind  and  power  of  any  ophthalmic  lens,  and  the 
position  of  its  optical  center. 

The  most  common  method  of  ascertaining  the  power  is  by 
neutralization  with  the  trial  lens  of  equal  denomination,  but  of 
opposite  sign. 

If  we  hold  a  convex  lens  in  front  of  the  eye  and  through  it 
look  at  a  distant  object,  an  image  of  the  object,  more  or  less  blurred 
will  be  seen.  If  the  optical  center  of  the  lens  lies  in  the  line  of 
vision,  no  lateral  displacement  will  result ;  but  if  the  lens  is  moved 
laterally  it  acts  like  a  prism  with  its  base  towards  the  center 
of  the  lens,  and  the  greater  the  lateral  movement,  the  greater  will 
be  the  prismatic  effect.  Since  a  prism  causes  an  apparent  displace- 
ment towards  its  apex,  it  follows  that  as  the  lens  is  moved  to  the 
right  the  object  appears  to  move  to  the  left,  and  vice  versa. 

On  the  other  hand,  if  a  concave  lens  is  substituted  for  the 


170  Errors  of  Refraction 

convex  lens,  the  object  will  appear  to  move  in  the  same  direction 
as  the  movement  of  the  lens. 

By  selecting  from  the  trial  case  that  lens  which  annuls  the 
lateral  deviation,  we  have  the  effect  of  plane-glass.  The  lens 
whose  power  is  sought  is  of  the  same  denomination  but  of 
opposite  sign  to  that  which  produces  this  effect. 

To  determine  the  position  of  the  center  of  the  lens,  we  view 
a  straight  line  (as  the  edge  of  a  test-card)  through  the  lens,  and 
observe  the  position  of  the  lens  in  which  there  is  no  break  in  the 
straight  line  as  seen  through  the  lens  and  beyond  its  borders. 
Marking  the  points  where  this  line  appears  to  cut  the  lens,  we 
connect  these  points  by  a  straight  line  drawn  in  ink.  This  line 
passes  through  the  center  of  the  lens.  Repeating  this  process  in 
another  meridian,  we  have  two  lines  passing  through  the  center,  and 
their  point  of  intersection  must  indicate  the  position  of  this  center. 

In  a  cylindrical  lens  the  lateral  deviation  takes  place  at  right 
angles  to  the  axis  of  the  lens,  and  any  line  making  an  oblique 
angle  with  this  axis  undergoes  an  angular  deviation,  the  explana- 
tion of  which  has  already  been  given  (p.  84).  Hence,  the  direction 
of  the  axis  is  determined  by  observing  that  direction  in  which  a 
lateral  movement  of  the  lens  produces  no  apparent  displacement 
of  an  object.  The  position  of  the  axis  is  determined  by  observing 
the  points  at  which  the  unbroken  line  (as  seen  through  the  lens 
and  beyond  its  edges)  cuts  the  lens;  the  straight  line  joining  these 
points  represents  the  axis  of  the  lens. 

We  may  also  determine  the  power  of  a  lens  by  direct  meas- 
urement of  the  curvature  of  its  surfaces  with  the  aid  of  a  lens- 
measure  or  spherometer. 

While  either  of  these  two  methods  may  be  used  with  satis- 
faction in  ophthalmological  practice,  each  of  them  may  lead  to 
false  deduction  unless  its  limitations  are  appreciated.  In  the  ap- 
plication of  neutralization  error  may  occur  from  neglect  of  the 
distance  between  the  optical  centers  of  the  two  lenses.  In  the 
stronger  lenses  this  error  is  considerable,  and  for  such  neutraliza- 
tion is  not  reliable,  except  in  piano-curved  lenses,  in  which  the  two 
curved  surfaces  may  be  placed  in  apposition.  In  the  use  of  the 
spherometer  error  is  liable  to  occur  from  the  variation  which  exists 
in  the  index  of  spectacle-glass  used  by  different  manufacturers: 
furthermore,  the  spherometers  which  are  commonly  sold  are  so 


Optometry   of   the  Refractive   Apparatus  171 

inaccurately  adjusted  that  they  cannot  be  relied  upon  to  denote 
fine  distinctions  of  lens  power. 

Cycloplegics. — Being  provided  with  test-letters  and  trial 
lenses,  we  have  still  another  matter  for  consideration  when  we 
undertake  to  make  use  of  this  method  of  examination.  It  is  our 
aim  to  determine  the  refraction  of  the  eye  with  the  ciliary  muscle 
in  a  state  of  complete  relaxation.  On  this  account  the  letters 
should  be  placed  not  less  than  five  meters  from  the  examinee; 
but  in  young  subjects  even  this  precaution  does  not  ensure  relaxa- 
tion, and  other  means  must  often  be  employed. 

Certain  drugs  possess  the  property  of  temporarily  paralyzing 
the  action  of  the  ciliary  muscle.  Since  they  also  dilate  the  pupil, 
they  were  formerly  called  mydriatics;  but  the  discovery  of  sub- 
stances such  as  cocain  and  euphthalmin,  which  dilate  the  pupil  but 
only  partially  affect  the  ciliary  muscle,  has  rendered  necessary  a 
means  of  distinction  between  drugs  which  dilate  the  pupil  and 
those  which  also  paralyze  the  ciliary  muscle.  The  latter  are  called 
cycloplegics. 

The  principal  cycloplegics  are  atropiu,  daturiu,  Iiyoscyamin. 
duboisiii,  scopalamiu  and  homatropin.  Of  these  the  effect  is  most 
persistent  in  the  case  of  atropin  (fifteen  days)  and  most  transient 
in  the  case  of  homatropin  (from  one  to  two  days).  Next  to 
homatropin  comes  scopalamin,  whose  effect  lasts  six  days,  being 
much  diminished  in  intensity  by  the  second  day.  Of  this  list  of 
drugs  two,  atropin  and  homatropin,  are  sufficient  for  routine  use 
in  the  determination  of  refraction. 

The  effect  of  belladonna,  from  which  the  alkaloid  atropin 
is  derived,  upon  the  pupil  and  the  accommodation  has  long  been 
known.  A  thorough  study  of  the  action  of  atropin  on  the  accom- 
modation was  made  by  Donders.  He  found  that  a  single  drop  of 
a  solution  containing  one  part  of  atropin  sulphate  £0  one  hundred 
and  twenty  parts  of  water  was  sufficient  to  produce  complete 
mydriasis  and  complete  cycloplegia  in  a  healthy  eye.  The 
mydriasis,  which  occurred  first,  reached  its  maximum  in  about 
twenty-five  minutes,  and  remained  stationary  for  thirty-six  hours, 
after  which  it  slowly  diminished,  the  pupil  regaining  its  normal 
size  in  about  fourteen  days.  The  cycloplegic  effect  was  scarcely 
noticeable  until  the  time  of  maximum  mydriasis,  when  accommo- 
dation rapidly  failed,  being  totally  paralyzed  at  the  end  of  one  and 
a  half  hours.    Total  paralysis  lasted  about  forty  hours;  after  this 


172  Errors  of  Refraction 

accommodative  power  gradually  returned,  regaining  its  full  ampli- 
tude after  the  expiration  of  about  twelve  days. 

The  weakest  solution  of  which  a  drop  will  cause  paralysis  of 
accommodation  is,  according  to  Jaarsma,  i  :i200.  The  duration 
of  this  action  is  twenty-four  hours,  while  the  effect  on  the  pupil 
lasts  for  ninety-six  hours.  The  same  author  states  that  one  drop 
of  a  solution  in  the  proportion  i  :8o,ooo  will  produce  mydriasis, 
the  effect  lasting  twenty- four  hours  (Landolt). 

Although  so  small  a  quantity  of  the  drug  suffices  to  produce 
its  maximum  effect  in  a  normal  eye,  several  instillations  should  be 
made  before  the  refraction  is  tested.  In  this  way  the  tendency 
to  spasmodic  contraction  of  the  ciliary  muscle,  which  is  so  fre- 
quently present  in  young  persons,  may  be  overcome.  A  one-half 
per  cent  solution  may  be  prescribed,  and  one  drop  of  this  should 
be  instilled  three  or  four  times  a  day  for  two  days  or  longer.  By 
this  means  constitutional  effects  of  the  drug  may  be  avoided  and 
relaxation  assured. 

There  sometimes  results  from  the  use  of  atropin  the  condition 
known  as  atropinism—an  irritation  and  inflammation  of  the  con- 
junctiva. It  usually  occurs  only  after  the  prolonged  use  of  the 
drug  in  inflammatory  states ;  seldom  from  the  brief  use  tor  testing 
refraction.  The  cause  of  this  condition  is  a  matter  of  doubt.  It 
is  thought  that  strongly  acid  or  alkaline  reaction  of  the  solution 
and  the  presence  of  micro-organisms  are  at  least  contributory 
elements.  Therefore,  the  solution  should  be  freshly  prepared  and, 
as  far  as  possible,  sterile. 

Because  of  the  great  persistence  of  the  effect  of  atropin,  it  is 
a  most  inconvenient  drug  for  use  in  refractive  work.  It  should, 
therefore,  be  reserved  for  those  cases  in  which  there  is  reason 
to  believe  that  homatropin  will  be  ineffective ;  that  is,  for  young 
children  and  for  those  adults  in  whom  complete  relaxation  has  not 
followed  the  use  of  the  latter  drug;  or,  again,  for  those  persons 
in  whom  it  is  desired  to  produce  a  prolonged,  enforced  rest  of  the 
accommodation. 

Homatropin  is  a  derivative  of  atropin,  being  obtained  from 
the  latter  through  a  complicated  chemical  process.  The  alkaloid 
is  an  oleaginous  liquid,  which  in  combination  with  hydrobromic 
acid  forms  a  crystallizable  salt,  and  it  is  this  salt  that  is  commonly 
used  in  ophthalmological  practice. 

Complete  relaxation  of  the  accommodation  may  be  obtained 


Optometry   of   the   Refractive  Apparatus  173 

with  homatropin-hydrobromate,  except  in  certain  cases  of  obsti- 
nate spasm,  such  as  occasionally  occurs  in  childhood,  and  in 
inflammatory  conditions.  In  those  cases  in  which  homatropin  is 
applicable  for  measuring  the  refraction,  relaxation  may  be  assured 
by  instilling  into  the  conjunctival  sac  one  or  two  drops  of  a  1.5  per 
cent  solution  every  ten  minutes  until  six  applications  have  been 
made.  In  one  hour  after  the  last  application  the  accommodation 
will  usually  be  entirely  paralyzed.  The  maximum  effect  on  the 
accommodation  lasts  not  more  than  a  few  hours,  and  at  the  expira- 
tion of  thirty-six  hours  near  work  may  usually  be  resumed. 

A  convenient  method  of  application  consists  in  the  use  of 
gelatin  disks,  as  recommended  by  Casey  JJ'ood.  A  variety  of 
drugs  may  be  thus  incorporated.  A  suitable  combination  for  the 
determination  of  refraction  consists  of  1/50  grain  of  homatropin 
(alkaloid)  and  1/50  grain  of  cocain-hydrochlorate.  One  disk  of 
this  composition  is  sufficient  to  insure  relaxation  except  in  unusual 
conditions.  In  children  a  second  disk  should  be  inserted  one  hour 
after  the  first  application.  The  cocain,  though  useless  alone  as  a 
cycloplegic,  increases  the  effect  of  the  homatropin. 

Method  of  Conducting  the  Test  with  Trial  Lenses. — 
In  making  use  of  the  test  by  trial  lenses  a  preliminary  examina- 
tion is  usually  conducted  without  cycloplegia. 

The  examinee  being  properly  seated,  and  the  other  conditions, 
as  described,  being  fulfilled,  he  is  asked  to  read  the  test-letters, 
beginning  with  the  largest  and  proceeding  to  successively  smaller 
letters  until  he  reaches  those  which  he  cannot  clearly  distinguish. 
If  at  a  distance  of  six  meters  he  can  read  all  the  letters  which,  as 
indicated  on  the  card,  are  intended  to  be  read  a,t  this  distance,  his 
vision  is  normal.  Normal  vision  is  possible  only  if  the  image  of 
the  letters  falls  accurately  upon  the  retina.*  The  eye  must,  there- 
fore, be  adapted  for  this  distance;  that  is,  there  is  1/6 D of  myopia. 
But  the  difference  in  position  of  the  retina  in  this  amount  of 
myopia  and  in  emmetropia  is  inappreciable,  and  we  regard  the 
eye  as  adapted  for  an  infinite  distance.  The  refractive  condition, 
therefore,  must  be  either  that  of  emmetropia  or  of  hyperopia  with 
exercise  of  accommodation. 

To  determine  which  of  these  two  conditions  is  present,  we 
place  before  the  eye  a  convex  spherical  lens  of  .50  D.     If  vision 


'Strictly  speaking,  a  slight  degree  of  ametropia  cannot  be  excluded  until  it  is 
proved  that  a  weak  lens  does  not  afford  still  better  vision,  for,  as  we  have  learned, 
in   many   cases  the   acuteness   reaches  6/4   or  even   6/3. 


174  Errors  of  Refraction 

is  not  rendered  worse  by  this  lens,  it  is  clear  that  accommodative 
action  has  been  replaced  by  the  convergent  power  of  the  lens.  To 
ascertain  whether  accommodation  is  still  being  exercised,  we  add 
stronger  and  stronger  lenses  until  we  obtain  the  strongest  lens 
which  does  not  render  vision  worse. 

Under  favorable  circumstances  the  accommodation  may  be 
totally  relaxed,  being  replaced  by  the  convex  lens,  and  the  dioptric 
power  of  this  lens  is  the  measure  of  the  hyperopia ;  but  frequently 
in  young  persons  a  spasmodic  condition  of  the  ciliary  muscle 
arises.*  If  this  condition  cannot  be  otherwise  excluded,  a  cyclo- 
plegic  must  be  employed. 

If,  in  relaxation  of  the  ciliary  muscle,  distant  vision  is  normal 
without  a  lens,  and  is  not  made  to  exceed  the  normal  standard 
by  the  addition  of  a  lens,  the  eye  is  emmetropic. 

If  the  vision,  having  been  found  normal  at  the  preliminary 
examination,  is  below  normal  in  cycloplegia,  there  is  either  hyper- 
opia or  astigmia  or  both.  If  vision  is  made  normal  with  the  aid 
of  a  convex  spherical  lens,  this  lens  measures  the  hyperopia;  but 
if  the  spherical  lens  does  not  improve  vision,  or  if,  while  it  im- 
proves vision,  it  does  not  render  it  normal,  astigmia  is  present. 
If  this  is  regular  it  may  be  corrected  by  means  of  a  cylindrical 
lens 

//  vision  is  below  normal  without  cycloplegia  we  must  differ- 
entiate between  five  possible  conditions. 

( i )  The  eye  may  be  hyperopic  and  without  sufficient  accom- 
modative power  to  focus  parallel  rays  upon  the  retina.  If  this  is 
so,  vision  will  be  rendered  normal,  or  at  least  improved,  by  means 
of  a  suitable  convex  spherical  lens. 

(2)  The  eye  may  be  emmetropic  or  hyperopic  with  an 
excess  of  accommodative  action ;  that  is,  the  condition  simulates 
myopia,  and  vision  will  be  rendered  worse  by  a  convex  lens  and 
improved  by  a  concave  lens. 

(3)  There  may  be  true  myopia. 

(4)  There  may  be  astigmia,  either  alone  or  in  combina- 
tion with  any  of  the  aforementioned  defects. 

(5)  The  defective  vision  may  be  due  to  no  error  of  refrac- 
tion, but  to  lack  of  transparency  of  the  media  or  to  anomaly  of 
the  retina,  optic  nerve,  or  brain. 

*  There  is  less  tendency  to  spasmodic  action  of  the  ciliary  muscle  when  both  eyes 
are  used  than  when  one  eye  is  excluded.  It  is  sometimes  advisable,  therefore,  to  make 
the   final    test   on    the    two   eyes    simultaneously. 


Optometry   of   the  Refractive  Apparatus  175 

Although  we  have  these  five  conditions  presenting  the 
common  symptom  of  defective  distant  vision,  it  is  not  difficult 
to  make  the  decision  as  to  which  of  these  conditions  exists. 

In  the  first  case,  the  fact  that  a  convex  spherical  lens  improves 
vision  reveals  hyperopia. 

In  the  second  case,  the  condition  will  be  suspected  in  a  young 
subject  and  the  accommodation  paralyzed,  when  the  true  condition 
of  hyperopia  or  emmetropia  will  appear. 

In  true  myopia,  as  in  the  previous  case,  vision  is  improved 
by  a  concave  spherical  lens.  Having  excluded,  either  by  cyclo- 
plegia  or  by  the  age  of  the  individual,  spasmodic  action  of  the 
accommodation,  we  place  before  the  eye  successively  stronger 
concave  lenses  until  we  obtain  that  lens  which  affords  normal  or 
maximum  vision.  This  lens  measures  the  degree  of  myopia.  But 
as  we  found  it  necessary  in  estimating  hyperopia  without  cyclo- 
plegia  to  select  the  strongest  convex  lens,  so,  under  the  same 
condition,  we  must  exercise  care  to  select  the  weakest  concave 
lens  which  affords  maximum  vision,  for  otherwise  the  myopia 
will  be  overestimated,  accommodation  being  exercised  to  over- 
come the  excessively  strong  concave  lens. 

The  next  and  last  of  the  refractive  errors  to  which  defective 
distant  vision  may  be  due,  is  astigmia.  We  suspect  this  when 
neither  a  convex  nor  a  concave  spherical  lens  affords  normal 
vision.  The  astigmia  may  be  regular  or  irregular.  The  former 
occurs,  as  we  have  learned,  when  there  is  asymmetry  of  one  or 
more  of  the  refracting  surfaces.  Pathological  irregular  astigmia 
is  most  frequently  the  result  of  corneal  inflammation,  whereby  the 
regularity  of  surface  has  been  destroyed.  Since  this  kind  of 
astigmia  cannot  be  corrected  by  a  lens,  its  determination  cannot 
be  accomplished  by  the  subjective  method  with  which  we  are  now 
concerned.  Our  attention  is  therefore  for  the  present  confined  to 
regular  astigmia. 

The  stenopaeic  disk  is  an  opaque  disk,  in  which  there  is  cut 
a  slit  1  mm  in  breadth  and  10  mm  in  length.  This  device  may 
be  used  for  determining  the  principal  meridians.  When  placed 
before  the  eye  the  stenopaeic  disk  permits  light  to  pass  into 
the  eye  unobstructed  in  the  direction  of  the  length  of  the  slit, 
while  at  right  angles  to  this  all  peripheral  rays  are  excluded. 
Practically  we  may  regard  all  the  entering  rays  as  lying  in  the 
meridian  which  corresponds  to  the   length  of   the   slit,   and  by 


176 


Errors  of  Refraction 


turning  the  slit  in  various  directions  we  can  find  that  meridian 
in  which  vision  is  best.  This  is  the  meridian  in  which  the  eye  is 
emmetropic,  or  most  nearly  so.  This  method  is  not  very  much 
used,  as,  owing  to  the  small  amount  of  light  which  can  enter  the 
eye,  the  normal  visual  acuity  is  not  attained. 

Another  device  for  the  detection  of  the  principal  meridians 
of  astigmia  is  a  chart  having  groups  of  parallel  lines  lying  in- 
different directions.  We  know  that  a  straight  line  appears  distinct 
to  an  astigmope  only  when  the  line  lies  at  right  angles  to  the 


fig.  85 

Clock    Dial    Chart 

meridian  in  which  it  is  accurately  focused,  and  that  the 
meridian  of  greatest  distinctness  is  that  in  which  the  refraction 
needs  correction.  If,  therefore,  we  have  groups  of  equally  distinct 
lines  radiating  from  a  center,  we  can  ascertain  the  principal 
meridians  from  the  relative  distinctness  with  which  the  groups 
of  lines  are  seen. 

Charts  of  this  kind  were  first  used  by  J  aval.  They  were  sub- 
sequently improved  and  elaborated  by  Green,  and  the  dial  shown 
in  Fig.  85  is  known  as  Green's  clock  dial  chart.  Other  charts 
similar  in  principle  to  the  clock  dial  are  also  used. 

In  this  method  of  finding  the  principal  meridians  we  place 
the  chart  at  a  distance  of  six  meters  from  the  examinee,  who  is 
directed  to  state  which  group  of  lines  appears  most  distinct.  If 
he  can  see  none  of  the  lines  clearly  we  endeavor  to  find  a  spherical 
lens — trying  convex  lenses  first — which  makes  one  group  of  lines 


Optometry   of   the  Refractive  Apparatus  177 

distinct.  The  group  at  right  angles  to  this  will  be  the  most 
indistinct  if  astigmia  exists,  and  these  two  groups  mark  the 
principal  meridians.  The  direction  in  which  the  lines  are  most 
indistinct  is  that  zvhich  is  corrected  by  the  spherical  lens. 

In  hyperopic  astigmia  many  persons  can  bring  first  one 
and  then  another  group  of  lines  into  distinctness  by  varying  the 
accommodation.  In  order  to  obviate  this,  resort  may  be  had  to 
the  fogging  system,  which  consists  in  over-correcting  the  hyperopia 
arid  noting  the  direction  in  which  the  lines  are  least  blurred  and 
that  in  which  they  are  most  so.  These  two  directions  mark  the 
principal  meridians,  and  by  a  gradual  reduction  of  the  over-correc- 
tion the  true  state  of  refraction  is  determined. 

If  the  principal  meridians  cannot  be  determined  with  cer- 
tainty in  this  way  we  must  resort  to  paralysis  of  the  accommoda- 
tion by  means  of  a  cycloplegic. 

Many  ophthalmologists  place  great  reliance  upon  the  clock 
dial  or  similar  chart ;  others  find  it  easier  to  determine  the  principal 
meridians  by  resorting  at  once  to  the  cylindrical  lens,  rotating  it 
before  the  eye  until  the  position  is  found  which  gives  the  greatest 
improvement  of  vision.  This  is  the  method  which  I  adopt,  as  I 
have  found  the  radiating  lines  unsatisfactory  in  practical 
work.  Many  persons  will,  from  inattention,  fail  to  note  a  differ- 
ence, even  in  marked  astigmia,  in  the  various  lines,  while  others 
will  never  acknowledge  that  all  are  alike  after  a  most  careful 
correction  of  the  refractive  error. 

Returning  now  to  our  example,  in  which  distant  vision  is 
defective  and  is  not  made  normal  by  any  spherical  lens,  we  pro- 
ceed to  ascertain  whether  astigmia  is  present.  We  may  begin 
by  using  the  stenopseic  disk  or  the  clock-face  chart,  or  we  may 
proceed  to  the  trial  of  cylindrical  lenses,  trying  first  convex  lenses. 

If  we  find  that  vision  is  improved  by  a  cylindrical  lens  we 
continue  the  process  until  we  find  the  lens  and  the  position  which 
afford  the  best  vision.  We  may  then  corroborate  the  result  with 
the  clock-face  chart — all  the  lines  should  be  clearly  seen  and  with 
equal  distinctness. 

In  astigmia  complicated  with  hyperopia  or  myopia  it  is  not 
always  easy  to  determine  the  exact  spherical  and  cylindrical 
elements  which  constitute  a  perfect  correction.  Having  obtained 
an  approximate  correction,  we  proceed  to  ascertain  whether  vision 
is  improved  by  the  addition  of  a  weak  convex  spherical  lens  (.25 


178  Errors  of  Refraction 

D  or  .50  D).  If  this  does  not  cause  improvement,  we  next  add  a 
weak  convex  cylinder,  axis  parallel  to  that  of  the  cylinder  already 
before  the  eye.  If  this  lens  does  not  improve  vision,  its  axis  is 
turned  at  right  angles  to  that  of  the  other  cylinder.  This  increases 
the  convexity  or  decreases  the  concavity  of  the  spherical  element, 
while  it  reduces  the  power  of  the  cylinder.  If  this  also  fails  to 
cause  improvement,  a  concave  cylinder  is  next  selected  and  placed 
first  with  its  axis  parallel  to  that  of  the  lens  already  found,  whereby 
the  convexity  of  the  cylindrical  element  is  diminished.  If  this 
does  not  cause  improvement,  the  axis  is  turned  through  ninety 
degrees,  whereby  the  convexity  of  the  spherical  element  is  dimin- 
ished, while  the  power  of  the  cylinder  is  increased.* 

If  a  change  in  the  cylinder  is  indicated  by  any  of  these  addi- 
tions, the  axis  of  this  revised  lens  must  be  shifted  slightly  until 
the  position  of  maximum  vision  is  obtained.  If  none  of  these 
additions  brings  vision  up  to  the  normal  standard,  we  finally  try 
the  experiment  of  reducing  the  spherical  convexity  by  adding  a 
weak  concave  spherical  lens.  If  normal  vision  cannot  be  obtained 
by  any  combination  of  spherical  and  cylindrical  lenses,  we  conclude 
that  there  exists  some  defect  which  is  incapable  of  correction  by 
lenses.  For  the  diagnosis  of  the  particular  condition  which  may 
be  present  other  methods  of  examination  must  be  employed. 

Notation  of  the  Axis  of  a  Cylindrical  Lens. — The 
position  in  which  a  cylindrical  lens  is  placed  is  indicated  by  the 
;angle  which  its  axis  makes  with  a  certain  fixed  line.  In  America 
the  usual  method  is  in  accordance  with  the  notation  of  angular 
magnitude  as  universally  employed  in  mathematical  science 
(Fig.  86),  and  an  American  optician  would,  unless  otherwise 
instructed,  use  this  notation  in  filling  an  order  for  lenses.f 

Other  systems,  which  are  used  in  Europe,  are  illustrated  in 
Figs.  87  and  88. 

Objective  Methods 

Since  our  aim  in  ascertaining  the  refractive  condition  is  to 
prescribe  suitable  lenses,  it  might  seem  as  if  the  foregoing  method, 
in  which  the  lenses  are  actually  placed  before  the  eye,  would 


•The  cylindrical  changes  may  be  made  with  the  crossed  cylinder  (Jackson).  This 
consists  of  a  convex  cylinder  (.25  D.)  combined  with  an  equal  concave  cylinder,  the 
two  axes  being  at  right  angles. 

t  If  there  is  a  probability  that  the  glasses  will  be  made  by  an  optician  of  one  of 
the   European   countries,   the   axes   should   be    diagrammatically   indicated. 


Optometry   of   the  Refractive  Apparatus 


179 


answer  all  requirements  for  the  selection  of  glasses ;  and,  in  truth, 
in  the  final  decision  as  to  the  proper  glass,  preference  must  ordi- 
narily be  given  to  this  test.     But,  owing  to  the  fact  that  many 


fig.  S6 

Ordinary  Method  of  Axis  Notation 

In  each  eye  the  position  of  the  axis  is  denoted  by  the  angle  which  it  makes  with 
the  horizontal  line,  this  angle  being  always  measured  from  the  right-hand  side  of  the 
observer  (left-hand  side  of  the  patient).  The  numbering  thus  runs  from  o°  to  1800, 
starting  at  the  nasal  side  in  the  right  eye  and  at  the  temporal  side  in  the  left  eye. 
The  horizontal   axis  is  always  denoted  by   1800    or  0°,   the  vertical  axis  by  900. 

patients  lack   intelligence,  and  that  some  purposely  mislead  the 
examiner,  and  to  other  difficulties,  it  is  of  the  utmost  importance 


fig.  87 

Symmetrical    System   of   Axis  Notation 

The  zero  line  is  horizontal,  and  the  deviation  of  the  axis  from  this  line  is  measured 
from  the   nasal  side   for  each  eye. 


FIG.    88 

Tempero-nasal   System   of  Axis  Notation 

The  zero  line  is  vertical,   and  the  deviation  of  the  axis  from  this  line  is  measured 
temporalward    (*)    or    nasalward    (n). 


that  we  should  be  able  to  determine  the  refraction  independently 
of  the  assertions  of  the  patient. 

The  first  of  these  objective  methods  is  that  in  which  use  is 
made  of  the  direct  method  of  ophthalmoscopy. 


i8o 


Errors  of  Refraction 


For  conducting  this  test  the  examiner  must  be  provided  with 
an  ophthalmoscope  of  at  least  moderate  completeness ;  that  is,  the 
instrument  must  be  equipped  with  a  sufficient  number  of  lenses 
to  enable  him  to  see  the  fundus  clearly,  without  any  exercise  of 
accommodation,  whatever  may  be  the  refraction  of  the  examining 
and  the  examined  eyes.  The  two  most  popular  instruments  for 
general  use  are  Loring's  (Fig.  89)  and  Morton's  (Fig.  90). 

In  the  explanation  of  the  principles  of  ophthalmoscopy  it  was 


fig.  89 

Loring's   Ophthalmoscope 

The  mirror  is  concave,  shaped  as  in  illustration,  with  a  central  perforation  ot 
4  mm  diameter,  and  so  attached  that  it  may  be  tilted  to  either  side.  The  focusing 
lenses  are  contained  in  a  full  disk  and  a  quadrant  of  a  disk,  the  one  revolving  over 
the  other,  so  that  by  suitable  combination  any  lens  required  for  neutralization  of  re- 
fractive error  can  be   obtained. 

shown  that  light  reflected  from  the  fundus  of  an  emmetropic  eye 
passes  out  of  the  eye  in  parallel  rays,  which  may  be  brought  to  a 
focus  on  the  retina  of  an  emmetropic  observer  without  exercise 


Optometry   of   the  Refractive  Apparatus 


181 


of  accommodation,  so  that  there  may  be  formed  on  his  retina  a 
clear  image  of  the  disk  and  blood  vessels  of  the  examined  eye. 

If  the  examined  eye  is  hyperopic,  light  from  its  fundus  leaves 
the  eye  in  divergent  pencils,  and  can  be  focused  by  an  emmetropic 
observer  only  by  the  aid  of  accommodation,  or  by  an  equivalent 
•convex  spherical  lens. 

If  the  examined  eye  is  myopic,  the  emergent  pencils  are  con- 


fig.  90 

Morton's    Ophthalmoscope 

In  this  instrument  the  lenses  are  set  in  a  cylinder  in  the  form  of  an  endless 
chain,  so  that  any  required  lens  may  be  readily  brought  to  the  sight  hole  by  meaiiis 
of    the    driving    wheel. 

vergent,   and   can  be   focused   on   the   retina  of   an   emmetropic 
observer  only  with  the  aid  of  a  concave  lens. 


182  Errors  of  Refraction 

In  applying  this  principle  in  practice  we  must  in  the  first 
place  be  assured  that  no  accommodation  is  exercised  by  the 
examining  or  the  examined  eye.  The  examiner  must  learn  by 
previous  practice  to  relax  his  accommodation  at  will ;  relaxation 
in  the  eye  under  examination  usually  occurs  during  ophthalmo- 
scopic examination,  provided  it  is  conducted  in  a  thoroughly 
darkened  room. 

These  conditions  being  fulfilled,  the  examiner  brings  the 
ophthalmoscope  and  his  eye  as  near  as  possible  to  the  eye  under 
examination.  The  ideal  position  would  be  such  that  the  ophthalmo- 
scopic lens  would  be  15  mm  in  front  of  the  examined  eye,  the 
position  at  which  trial  lenses  are  placed  in  the  subjective  exami- 
nation. So  close  an  approximation  is  not  possible,  but  we  do  not 
incur  a  noteworthy  error  by  our  failure  to  reach  this  position. 
The  examiner  now  looks  at  the  small  vessels  which  lie  on  the 
outer  side  of  the  optic  disk,  tracing  them  as  far  as  possible  towards 
the  macula,  since  it  is  the  macular  region  whose  refraction  we  wish 
to  determine.  The  strongest  convex  or  the  weakest  concave  lens 
with  which  these  vessels  appear  distinct  measures  the  degree  of 
ametropia  if  the  examiner  is  emmetropic.  When  the  latter  is 
ametropic  and  his  refractive  error  is  not  corrected  the  dioptric 
power  of  his  correcting  lens  must  be  subtracted  from  that  of  the 
ophthalmoscopic  lens  with  which  the  vessels  appear  distinct. 

If  -j-5  D  is  the  strongest  lens  with  which  the  retinal  vessels 
are  seen  distinctly  and  if  the  examiner  has  2  D  of  hyperopia,  it 
is  evident  that  2  D  of  the  ophthalmoscopic  lens  is  required  for  the 
correction  of  the  examiner's  hyperopia,  leaving  3  D  as  the  degree 
of  hyperopia  in  the  examined  eye.  If  the  examiner  has  2  D  of 
myopia,  while,  as  above  -j-5  D  is  the  power  of  the  lens  which 
makes  the  retinal  vessels  distinct,  the  hyperopia  of  the  examined 
eye  is  7  D.  Subtracting  — 2  D,  the  lens-equivalent  of  the  exam- 
iner's myopia,  is  the  same  as  adding  -j-  2  D.  In  other  words,  the 
examiner's  myopia  (2  D)  neutralizes  2  D  of  the  hyperopia 
of  the  examined  eye,  and  this  added  to  5  D  of  hyperopia  neutral- 
ized by  the  ophthalmoscopic  lens,  makes  a  total  hyperopia  of  7  D. 
Similarly,  if  the  vessels  appear  distinct  with  — 5  D,  the  examiner 
having  2  D  of  myopia,  the  myopia  of  the  examined  eye  is  3  D; 
and  if  the  examiner  has  2  D  of  hyperopia,  the  vessels  still  being 
distinct  with  — 5  D,  the  myopia  of  the  examined  eye  is  7  D. 

When   the   examiner   has   considerable   astigmia,    it    is   be^t 


Optometry   of   the  Refractive  Apparatus  183 

for  him  to  have  his  correcting  lens  attached  to  the  ophthalmoscope 
so  that  this  lens  may  be  used  in  combination  with  the  spherical 
lenses  of  the  instrument. 

The  same  principle  is  applicable  in  the  determination  of 
astigmia ;  but  in  this  case  it  will  be  noticed  that  when  the  vessels 
running  in  a  certain  direction  appear  distinct,  those  running  in  a 
direction  at  right  angles  to  this  will  be  blurred.  These  two  direc- 
tions mark  the  principal  meridians  of  the  astigmia.  In  accord- 
ance with  the  principles  which  we  have  learned,  we  know  that  the 
meridian  in  which  the  vessels  are  most  blurred  is  that  which  is 
corrected  by  the  ophthalmoscopic  lens.  After  the  number  of  this 
lens  has  been  noted,  the  vessels  at  right  angles  to  the  first  are 
next  made  to  appear  distinct.  The  difference  between  the  power 
of  the  first  and  second  lenses  represents  the  degree  of  astigmia. 

Much  practice  and  skill  are  requisite  for  determining  accu- 
rately the  meridians  and  degree  of  astigmia  by  this  method, 
and,  as  a  practical  test,  it  has  been  largely  replaced  by  skiascopy 
and  ophthalmometry. 

Indirect  Method  of  Ophthalmoscopy. — Since  there  is 
formed  at  the  far-point  of  a  myopic  eye  an  aerial  image  of  the 
optic  disk  and  retinal  vessels,  the  distance  of  this  image  from  the 
eye  furnishes  a  means  of  determining  the  degree  of  myopia.  In 
emmetropic  and  hyperopic  eyes  the  same  method  is  applicable  by 
adding  a  strong  convex  lens,  as  used  in  indirect  ophthalmoscopy. 
This  method,  like  many  of  the  older  tests,  is  not  convenient  in 
practical  work,  since  it  is  not  possible,  without  a  special  contriv- 
ance, to  determine  with  precision  the  place  at  which  the  aerial 
image  is  formed. 

Skiascopy. — This  method  is  so  simple  in  application  and 
so  accurate  in  results  that  it  surpasses  all  other  objective  means  of 
measuring  refraction.  Bozvman,  in  1859,  first  employed  skiascopy 
for  the  detection  of  irregular  astigmia  in  conical  cornea.  Cuignet, 
in  1876,  introduced  it  as  a  test  for  all  refractive  errors  under  the 
name  keratoscopie.  The  first  explanations  of  the  optical  principles 
involved  were  given  by  Landolt,  who  suggested  the  name  pupillo- 
scopie,  and  by  Parent,  who  adopted  the  name  retinoscopie.  The 
latter  also  introduced  the  practice  of  placing  the  correcting  lens  in 
front  of  the  eye,  thereby  giving  the  test  its  practical  value  in  esti- 
mating the  degree  of  ametropia.     The  earlier  names  being  mani- 


184  Errors  of  Refraction 

festly  unsuitable,  Priestly-Smith,  in  1884,  recommended  the  term 
shadozv-test,  upon  which  is  based  the  simple  word  skiascopy. 

The  necessary  appliances  for  the  application  of  skiascopy 
are  a  suitable  lamp,  a  plane  or  concave  mirror,  and  a  set  of  trial 
lenses.*  An  Argand  gas  burner  or  a  frosted  electric  lamp,  mounted 
on  an  adjustable  bracket,  gives  suitable  illumination,  or  a  minia- 
ture electric  lamp  may  be  attached  directly  to  the  mirror.  The 
amount  of  light  may  be  regulated  by  an  opaque  chimney  having 
an  opening  in  its  side.  The  size  of  this  opening  should  vary  with 
the  position  of  the  light.  When  this  is  behind  the  patient,  as  is 
the  case  in  the  use  of  the  concave  mirror,  the  opening  should  be  2 
cm  or  3  cm  in  diameter ;  in  fact,  the  opaque  shade  is  in  this  case 
not  essential.  But  when  the  light  is  in  front  of  the  patient  and 
near  the  eye  of  the  examiner,  this  being  the  most  advantageous 
arrangement  in  the  use  of  the  plane  mirror,  the  shade  is  indis- 
pensable, and  the  opening  should  not  be  more  than  10  mm  in 
diameter.  Since  we  often  wish  to  vary  the  position  of  the  light 
relatively  to  the  mirror,  a  convenient  arrangement  is  a  rotating 
disk,  with  openings  of  different  sizes,  any  one  of  which  may  be 
used ;  or  we  may  employ  the  iris-diaphragm,  as  in  Thorington's 
adjustable  diaphragm  chimney  (Fig.  91). 

The  mirror,  being  circular  in  form,  should  have  at  its  center 
a  circular  sight-hole  2  mm  in  diameter;  the  mirror  itself  should  be 
from  2  cm  to  3  cm  in  diameter  if  plane,  and  somewhat  larger 
(3  cm  to  4  cm)  if  concave.  The  focal  length  of  the  concave 
mirror  should  be  about  25  cm. 

The  lenses  may  be  taken  from  the  trial-case,  any  desired  lens 
being  supported  in  the  trial-frame,  and  placed  before  the  eye 
under  examination ;  or,  they  may  be  arranged  in  a  disk  in  such 
manner  that  any  desired  lens  may  be  quickly  brought  before  the 
eye. 

The  room  in  which  the  examination  is  made  should  be  thor- 
oughly darkened  as  for  ophthalmoscopy,  and  if  the  pupil  is  small, 
cocain,  euphthalmin,  or  homatropin-  should  be  used.f 

The  examinee  and  examiner  are  seated  facing  each  other  as 
for  opthalmoscopy,  the  distance  between  the  two  being  usually 
one  meter.    The  examinee  is  instructed  to  look  slightly  to  the  right 


*A  tape-measure  for  determining  the  distance  between  the  patient  and  the  observer 
is  also   useful. 

t  If  the  luminous  (electrically  lighted)  skiascope  is  used,  artificial  dilation  of  the 
pupil  is   seldom   required. 


Optometry   of  the   Refractive   Apparatus 


185 


or.  left  of  the  examiner's  head,  according  as  the  right  or  left  eye 
is  under  examination,  while  the  examiner  throws  the  light  reflected 
from  the  lamp  into  the  eye  of  the  examinee.  The  examiner  then, 
looking  through  the  sight-hole  of  the  mirror,  perceives  the  light- 
reflex  coming  from  the  region  between  the  optic  disk  and  macula 
of  the  examined  eye.  Examination  of  the  macular  region  is  not 
possible  because  of  annoying  reflexes ;  but  our  aim  should  always 
be  to  have  this  region  as  little  as  possible  removed  from  the  line 
of  vision,  since  the  refraction  of  other  parts  of  the  eye  sometimes 


fig.  91 

Iris   Diaphragm   Chimney 

differs  materially  from  this  portion,  which  alone  is  concerned  in 
distinct  vision. 

The  manner  of  measuring  the  ametropia  by  this  method  is 
best  explained  by  means  of  illustrative  examples. 

Let  us  suppose,  for  instance,  that  with  a  plane  mirror, 
held  one  meter  from  the  eye  under  examination,  the  pupil  appears 
brightly  illuminated,  and  that  on  rotating  the  mirror  the  light 
reflex  is  followed  by  a  slightly  curved  shadow  which  quickly 
covers  the  entire  pupil.  We  know  that  we  are  near  the  point  of 
reversal;  that  is,  the  eye  has  about  one  diopter  of  myopia  (Fig. 
92).  If  the  rapidly  moving  shadow  travels  in  the  diiection  of 
rotation  of  the  mirror,  the  myopia  is  slightly  less  than  1  D ;  if  it 
travels  in  the  opposite  direction,  the  myopia  is  slightly  in  excess 


186  Errors  of  Refraction 

of  i  D.  By  moving  forward  or  backward  we  may  find  the  posi- 
tion at  which  no  appreciable  shadow  is  observed,  and  by  noting 
the  distance  from  the  eye  the  amount  of  myopia  may  be  estimated. 
Or  by  adding  a  weak  lens,  convex  or  concave  according  as  the 
direction  of  the  shadow  is  with  or  against  the  direction  of  rotation, 
we  select  that  lens  which  neutralizes  the  shadow  movement.  The 
lens  which  produces  this  effect  creates  an  artificial  myopia  of  I  D.. 

If  a  convex  lens  of  .50  D  is  required  to  produce  this  result, 
the  eye,  having  1  D  of  myopia  with  the  lens,  must  have  .50  D 
of  myopia  without  the  lens.  If  a  concave  lens  of  .50  D  is  required 
to  neutralize  the  shadow  movement  the  eye  has  without  the  lens 
1.50  D  of  myopia. 

When,  on  rotating  the  mirror  in  any  direction,  the  shadow 
moves  slowly  across  the  pupil  in  the  direction  of  rotation  of  the 
mirror,  the  reflex  being  dull,  the  eye  is  highly  hyperopic.  We 
place  a  4  D  convex  lens  before  the  eye,  and  note  that  the  shadow 
moves  more  rapidly,  but  still  in  the  direction  of  rotation.  We 
substitute  a  convex  lens  of  6.50  D,  and  the  shadow  now  moves 
rapidly  in  the  direction  opposite  to  the  rotation.  We  therefore 
take  a  weaker  lens  (6'Dj  and  find  that  there  is  now  no  appre- 
ciable shadow :  hence,  this  lens  produces  1  D  of  myopia,  and  the 
eye  without  the  lens  must  have  5  D  of  hyperopia. 

If  the  reflex  is  dull  and  moves  slowly  in  the  opposite  direc- 
tion to  the  rotation,  the  eye  is  highly  myopic.  We  may  estimate 
the  degree  of  myopia  roughly  by  moving  towards  the  examinee 
until  we  reach  the  point  of  reversal.  If  this  is  one-tenth  of  a 
meter  from  the  examined  eye  there  exists  10  D  of  myopia;  but  as 
it  is  difficult  to  ascertain  the  exact  point  of  reversal,  and  as  a  slight 
inaccuracy  will  make  a  difference  of  several  diopters  in  high 
myopia,  it  is  better  to  place  before  the  eye  a  concave  lens  which 
will  bring  the  point  of  reversal  to  a  more  convenient  position, 
one  meter  from  the  eye.  At  this  distance  the  error  resulting 
from  misjudging  the  exact  point  of  reversal  is  slight.  We,  there- 
fore, in  this  case  place  before  the  eye  a  concave  spherical  lens  of 
10  D  and  resume  our  former  position,  one  meter  from  the  eye. 
We  notice  that  the  shadozv  moves  with  the  rotation;  we  substitute 
a  weaker  lens  (9D)  and  with  this  the  shadow  disappears.  Since 
a  concave  lens  of  9  D  neutralizes  all  but  1  D  of  the  myopia  in  this 
eye,  the  eye  without  the  lens  must  have  myopia  of  10  D. 

The  next  example  is  that  in  which  the  shadow  moves  with 


Optometry   of   the  Refractive  Apparatus  187 

the  rotation  in  all  meridians,  but  more  rapidly  in  the  vertical  than 
in  the  horizontal  meridian.    By  placing  a  convex  spherical  lens  of 

1  D  before  the  eye  the  shadow  is  caused  to  disappear  in  the 
vertical  meridian,  but  in  the  horizontal  meridian  the  light  and 
shadow  still  travel  in  the  direction  of  rotation.  The  edge  of  the 
shadow  will  be  straight,  or  nearly  so  (Fig.  93),  and  the  direction 
of  this  edge  marks  the  direction  of  the  axis  of  the  cylindrical  lens 
which  corrects  the  astigmia. 

We  now  place  before  the  eye,  in  addition  to  the  I  D  sphere,  a 
convex  cylindrical  lens  of  2  D,  axis  vertical.  With  this  lens 
no  shadow  is  noticed  in  any  meridian.  Since  the  convex  lens 
of  1  D  is  required  to  produce  1  D  of  myopia  in  the  vertical 
meridian,  the  eye  is  emmetropic  in  this  meridian.  In  the  hori- 
zontal meridian  the  combined  action  of  the  spherical  and  cylin- 
drical lenses  is  necessary  to  produce  1  D  of  myopia.  The  com- 
bined strength  of  these  two  lenses  in  the  horizontal  meridian  is- 
3  D;  in  this  meridian  therefore  there  is  2  D  of  hyperopia  without 
the  lenses.     There  is  in  this  eye  simple  hyperopic  astigmia  of 

2  D. 


o 


FIG.  92  FIG.   93  FIG.  94 

fig.   92. — Showing  the   form   of  the   shadow   in   hyperopia,    emmetropia,   or   myopia- 
fig.    93. — Showing    the    rectilinear    shadow   in    astigmia    when    the    examiner,    being, 
near  the  point  of  reversal  of  one  principal  meridian,  tilts  the  mirror  to  one  side. 
fig.   94. — Showing  the  central  band  of  light  in  astigmia. 

Further  examples  are  unnecessary  illustrating  compound 
astigmia  (both  principal  meridians  being  hyperopic  or  both 
myopic)  and  mixed  astigmia  (one  principal  meridian  being" 
hyperopic  and  the  other  myopic),  since  the  method  of  procedure 
is  the  same  in  all  cases.  The  point  of  reversal  for  one  principal 
meridian  is  first  brought  to  the  position  of  the  examiner  with  the 
aid  of  a  spherical  lens,  and  then  by  the  addition  of  a  proper 
cylindrical  lens  the  point  of  reversal  for  the  other  principal  meri- 
dian is  brought  to  the  same  position.* 

In  the  higher  degrees  of  astigmia,  and  also  in  the  lower 
degrees  by  exercising  the  proper  precautions  (p.  97),  we  may 
see  the  characteristic  band  of  light  (Fig.  94). 

*Or  each  meridian  may  be  separately  corrected  by  a  spherical  lens.     The  difference: 
in   power  between  the  two  lenses  represents  the  astigmia. 


1 88  Errors  of  Refraction 

The  student  who  has  mastered  the  principles  of  the  test 
with  the  plane  mirror  will  have  no  difficulty  in  the  substitution 
•of  the  concave  mirror.  As  has  already  been  explained,  the  move- 
ment of  the  light  and  shadow  with  the  concave  mirror  is  opposite 
to  that  with  the  plane  mirror ;  that  is,  the  motion  is  against  the 
rotation  of  the  mirror  in  hyperopia  and  with  this  rotation  in 
myopia. 

Another  matter  which  must  be  remembered  in  the  substitu- 
tion of  the  concave  for  the  plane  mirror  is  that  in  the  former 
the  apparent  source  of  illumination  is  the  aerial  image,  situated  in 
front  of  the  mirror,  whereas  in  the  latter  the  apparent  source  of 
illumination  is  behind  the  mirror.  With  the  concave  mirror  the 
aerial  image  cannot  lie  nearer  the  mirror  than  the  principal  focus, 
and  with  the  approach  of  the  lamp  to  the  mirror  the  aerial  image 
recedes  from  the  mirror. 

The  ideal  arrangement  is  such  that  the  apparent  source  of 
illumination  and  the  observer  are  at  the  same  distance  from  the 
examined  eye;  and,  at  any  rate,  that  the  relation  between  these 
two  is  constant.  With  the  plane  mirror  the  apparent  source  of 
illumination  may  be  brought  near  the  observer  by  placing  the 
lamp  very  near  the  mirror,  the  observer  moving  the  lamp  as  he 
moves  his  position ;  or  he  may  have  a  miniature  electric  lamp 
attached  to  the  mirror.  Hence,  with  the  plane  mirror  the  ex- 
aminer may  vary  his  position  at  his  convenience.  He  may  thus 
estimate  the  ametropia  with  few  changes  of  lenses.  But  when 
the  concave  mirror  is  used,  alterations  in  the  illumination  of  the 
pupil,  due  to  the  variation  in  position  of  the  aerial  image,  are  so 
great  as  to  render  the  test  unsatisfactory  unless  the  observer 
selects  a  fixed  position  for  himself  and  the  lamp.  The  lamp 
should  be  behind  and  he  should  be  one  meter  in  front  of  the 
examinee. 

Difficulties  in  the  Application  of  Skiascopy. — Although  the 
phenomena  of  skiascopy  are  characteristic,  yet  when  we  come  to 
employ  this  method  of  examination  in  practice,  we  frequently  meet 
with  difficulties  which  arise  from  imperfections  in  the  optical  con- 
struction of  the  eye. 

The  chief  disturbing  element  is  aberration.  Since  in  normal 
eyes  the  refracting  surfaces  are  approximately  portions  of 
spherical  surfaces,  the  light  which  passes  near  the  center  of  the 
pupil  is  less  highly  refracted  than  that  which  passes  along  the 


Optometry   of   the  Refractive  Apparatus  189 

periphery.  Hence,  when  the  examiner  is  at  the  point  of  reversal 
for  the  central  area,  he  will  be  without  that  for  the  peripheral  part 
of  the  widely  dilated  pupil.  If  the  aberration  is  abnormally  great, 
he  may  see  clearly  the  shadow  at  the  periphery  move  in  one  direc- 
tion, while  that  at  the  center  moves  in  the  opposite  direction.  As 
the  central  area  is  the  part  concerned  in  normal  vision,  the  exam- 
iner should  ascertain  the  point  of  reversal  for  this  part  of  the 
pupil,  disregarding  the  movement  at  the  periphery. 

The  aberration  just  described  is  ordinary  spherical  or  positive 
aberration ;  it  is  the  form  which  usually  occurs  in  the  eye.  But 
the  opposite  or  negative  aberration  sometimes  occurs.  This  is 
the  rule  in  conical  cornea,  for  in  this  condition  the  curvature  of 
the  cornea  is  much  greater  at  the  center  than  at  the  periphery. 

It  was  the  effect  of  aberration  in  conical  cornea  that  attracted 
the  attention  of  Bowman.  When  in  this  affection  the  observer  is 
at  the  point  of  reversal  for  the  periphery  he  will  be  far  removed 
from  this  point  for  the  center  of  the  pupil.  The  shadow  at  the 
center  will  therefore  move  slowly  while  that  at  the  periphery  will 
move  rapidly,  presenting  the  appearance  of  a  central  light  area 
encircled  by  a  swiftly  moving  peripheral  shadow. 

Another  difficulty  in  the  application  of  skiascopy  is  that  which 
arises  from  irregular  astigmia.  This  exists,  to  a  certain  extent, 
in  all  eyes.  A  careful  observation  of  the  shadow  when  the  ex- 
aminer is  near  the  point  of  reversal  will  reveal  this  by  the  faint 
conflicting  shadows  moving  in  various  directions.  When  the 
irregular  astigmia  is  more  pronounced,  these  shadows  are  so 
marked  as  to  interfere  seriously  with  the  estimation  of  the  refrac- 
tion at  the  center  of  the  pupil.  This  is  especially  so  in  eyes  whose 
corneas  have  been  the  seat  of  inflammation  or  ulceration,  whereby 
the  regularity  of  surface  has  been  destroyed.  There  is  no  one 
point  of  reversal  for  such  eyes,  and  distinct  vision  is  not  obtainable. 

A  peculiar  appearance,  described  by  Jackson  as  the  scissors 
movement,  is  sometimes  seen.  This  movement  appears  when  in 
any  direction  the  eye  is  more  highly  refracting  in  one-half  of 
the  pupillary  area  than  in  the  other  half.  Thus,  if  the  examiner 
is  within  the  point  of  reversal  for  the  upper  part  of  the  pupil  and 
without  this  point  for  the  lower  part,  rotation  of  the  mirror  will 
cause  the  two  shadows  to  move  towards  or  away  from  the  center 
of  the  pupil.  Since  the  appearance  resembles  the  opening  and 
shutting  of  a  pair  of  scissors,  it  has  received  therefrom  its  name. 


190  Errors  of  Refraction 

In  order  to  obtain  a  clear  conception  of  these  various  appear- 
ances and  to  obtain  the  requisite  skill  for  the  practical  application 
of  skiascopy,  the  student  should  procure  a  skiascopic  eye  (Fig.  95), 
constructed  for  this  purpose,  and  thoroughly  familiarize  himself 
with  the  phenomena  which  are  to  be  observed  in  various  grades 
of  ametropia.  Having  accomplished  this,  he  is  prepared  to  make 
further  studies  upon  living  eyes,  selecting  at  first  those  which  are 
free  from  marked  irregularities.  He  should,  if  possible,  conduct 
the  examination  with  a  moderately  dilated  pupil,  so  as  to  avoid 
the  aberration  and  irregular  astigmia  commonly  present  at  the 
periphery  when  the  pupil  is  widely  dilated. 

Ophthalmometry. — Ophthalmometry,  in  the  commonly  ac- 
cepted meaning  of  the  word,  consists  in  determining  the  corneal 
astigmia  by  direct  measurement  of  the  corneal  curvature. 

When  there  is  a  very  decided  asymmetry  or  irregularity  of 
the  cornea,  it  may  be  detected  with  Placido's  disk  (Fig.  96), 
which  consists  of  a  series  of  concentric  circular  rings  painted  on 
a  metal  disk  having  a  hole  in  the  center.  The  observer,  looking 
through  this  hole,  reflects  light  from  the  disk  to  the  cornea 
under  examination  while  he  observes  the  reflected  image  of  the 
rings  as  formed  at  the  anterior  surface  of  the  cornea.     In  marked 


fig.  95 

Eye  Model  for  the  Practice  of  Skiascopy 


regular  astigmia  the  image  of  the   rings   appears   oval,  and   in 
irregular  astigmia  the  image  is  distorted. 

But  for  the  accurate  measurement  of  the  cornea  the  ophthal- 
mometer is  used.  (Fig.  97.)  The  principle  on  which  this  in- 
strument is  constructed  has  already  been  described  in  Part  I. 


Optometry   of   the   Refractive   Apparatus 


191 


In  the  application  of  ophthalmometry  the  person  to  be  ex- 
amined, being  properly  seated  before  the  instrument,  the  fore- 
head   supported     in    the     frame     provided     for     that     purpose, 


FIG.    96 
Placido's   l'isk 


and  the  eye  not  under  examination  being  covered  by  the  blind 
attached  to  the  head-rest,  the  operator  adjusts  the  tube  of  the 
telescope  while  the  examinee  looks  directly  into  the  tube,  taking 
care  to  keep  the  eye  wide  open,  the  two  eyes  on  a  level,  and  the 
forehead  firmly  resting  in  the  frame.  The  operator  then  looking 
through  the  telescope  sees  the  double  images  of  the  mires  reflected 
from  the  cornea.  If  these  are  blurred,  they  are  brought  into 
focus  by  proper  adjustment  of  the  telescope.  The  instrument  is 
then  still  further  adjusted  vertically  or  horizontally  so  that  the  two 
inner  images  are  brought  into  the  center  of  the  field  of  view,  the 
two  lateral  images  being  disregarded.  After  this  is  accomplished 
the  instrument  is  revolved  until  the  axial  lines  of  the  images  show 
a  single  straight  and  unbroken  line.  If  there  is  no  corneal 
astigmia  this  condition  will  exist  in  all  meridians ;  otherwise  in 
only  two  meridians — the  principal  meridians  of  the  cornea,  or 
the  axes  of  the  astigmia. 


192 


Errors  of  Refraction 


An  axis  having  been  thus  ascertained,  the  primary  position 
(Fig.  98)  is  obtained  by  appropriate  adjustment  and  the  corneal 
refraction  (in  diopters)  is  noted.  The  tube  and  mires  are  next 
rotated,  and  the  departure  from  the  axial  position  is  indicated 
in  an  asymmetrical  cornea  by  a  break  in  the  axial  lines. 

When  the  rotation  has  been  carried  through  900  the  axial 
lines  are  again  continuous.*  If  in  this,  the  secondary  position, 
there  is  an  overlapping  of  the  mires  (Fig.  99),  the  astigmia  may 


fig.  97 

The     ophthalmometer     as     adapted     for     measuring     both     corneal     and     lenticular 
astigmia. 


be  measured  by  the  amount  of  overlapping  (Javal-Schiots) ,  or 
the  images  may  be  again  brought  into  the  contact  position  and 
the  astigmia  measured  by  noting  the  difference  in  reading  of  the 
scale  in  the  two  meridians.  If  in  the  secondary  position  there  is 
a  separation  of  the  mires,  they  should  be  brought  into  the  contact 
position  and  the  reading  noted,  or,  after  obtaining  the  contact 
position,  the  instrument  may  be  revolved  into  the  first  found 
meridian,  when  there  will  be  an  overlapping  of  the  mires. 

If  the  first  meridian  is  horizontal  or  nearly  so,  while  the 
mires  overlap  in  the  vertical  meridian,  the  astigmia  is  with  the 
rule  {direct),  and  if  the  mires  are  separated  in  the  vertical  meri- 
dian the  astigmia  is  against  the  rule  (indirect). 


*As  the  curvature  of  the  cornea  lacks  mathematical  accuracy,  the  two  meridians 
are  not  ahvavs  exactly  at  right  angles,  but  their  deviation  from  this  relation  is  very- 
slight. 


Optometry   of  the  Refractive  Apparatus 


193 


In  the  use  of  the  ophthalmometer  it  is  essential  that  the  eye 
under  examination  be  maintained  in  a  fixed  position  during  the 
process  of  measurement,  for  the  result  is  of  little  value  if  this 
precaution  is  not  taken.  We  should  be  assured  that  we  are 
measuring  the  curvature  in  the  pupillary  area. 

There  are  several  reasons  zvhy  the  ophthalmomctric  record 
frequently  fails  to  agree  with  the  subjective  astigmia.    One  cause 


fig.  98 

Primary  Position. 


FIG.    99 

Secondary     Position — overlapping     of 
the    mires. 


for  this  disagreement  is  the  lack  of  care  in  making  the  measure- 
ments under  the  precautions  just  mentioned.  In  fact,  without 
more  cooperation  than  some  patients  are  able  to  give,  a  reliable 
ophthalmometry  reading  is  impossible. 

Another  cause  for  this  disagreement  is  that  we  measure  a 
very  small  part  of  the  pupillary  area  of  the  cornea,  while  in  other 
portions  of  this  area  the  curvature  differs  from  that  which  we. 
measure. 

The  refractive  effect  of  the  posterior  surface  of  the  cornea 
is  also  an  uncertain  factor;  but  if  this  surface  follows  the  con- 
formation of  the  anterior  surface,  as  is  probable,  there  is  no 
appreciable  error  from  the  neglect  of  this  refraction. 

Disappointment  in  the  use  of  the  ophthalmometer  is  also  due 
to  the  failure  on  the  part  of  the  examiner  to  bear  in  mind  that 
there  is  in  high  degrees  of  symmetrical  ametropia  a  wide  variance 
between  the  astigmia  as  measured  at  the  corneal  surface  and 
its  correcting  lens  placed  at  a  distance  of  75  mm  from  the  cornea. 
The  explanation  of  this  discrepancy  will  be  found  in  the 
appendix. 

Finally  the  disagreement  between  the  subjective  astigmia 
and  the  keratometric  record  may  be  due  to  asymmetry  of  the 
crystalline  lens. 

In  the  application  of  keratometry  we  are  taught  to  deduct 
.50  D    from   the   corneal    astigmia   if   this   has   its   meridian   of. 


3  04  Errors  of  Refraction 

greatest  refraction  vertical,  and  to  add  this  amount  if  the  meridian 
of  greatest  refraction  is  horizontal.  The  reason  usually  given 
tor  this  empirical  rule  is  that  the  Obliquity  of  the  crystalline  lens 
produces  .50  D  of  astigmia'  with  its  meridian  of  greatest  re- 
fraction lying  in  or  near  the  horizontal  plane.  In:  order  that  this 
amount  of  asymmetry  may  be  effected  by  the  oblique  position  of 
the  lens;  the  angle  alpha  must  be  about  ten  degrees,  whereas  it  is 
usually  not  more  than  five  degrees.  This  amount  of  obliquity  pro- 
duces a  little  more  than  one-eighth  of  a  diopter  of  astigmia.  We 
must  therefore  look  elsewhere  for  the  common  discrepancy  of 
,50  D  between  the  keratometric  record  and  the  subjective 
astigmia. 

In  the  application  of  my  ophthalmometer  I  have  found  that 
this  discrepancy  is  almost  always  due  to  asymmetry  of  the 
posterior  surface  of  the  lens.  Not  infrequently  the  astigmia  of  this 
surface  reaches  1  D,  or  even  more.  In  other  instances  the  surface 
is  symmetrical.  We  cannot  therefore  formulate  any  general  rule 
as  to  the  amount  of  the  crystalline  astigmia  which  is  to  be  added 
to  or  subtracted  from  the  keratometric  record. 

Owing  to  the  larger  radius  of  the  anterior  surface  of  the 
lens  a  high  degree  of  asymmetry  is  required  to  produce  an  appre- 
ciable amount  of  astigmia.  The  highest  amount  which  I  have 
measured  is  .75  D.  In  the  large  majority  of  cases  the  amount 
is  less  than  .25  D. 

In  the  measurement  of  the  anterior  surface  of  the  lens  the 
eye  must  be  under  the  influence  of  a  mydriatic  (a  cycloplegic  in 
yOung  persons),  but  this  is  not  necessary  in  the  case  of  the 
posterior  surface. 

In  view  of  the  difficulties  and  uncertainties  of  ophthalmom- 
etry many  ophthalmologists  think  that  this  method  of  examination 
has  so  little  practical  value  that  it  does  not  repay  the  examiner  foi 
the  time  expended  in  its  application.  My  own  opinion,  however; 
is,  that  if  used  with  a  proper  appreciation  of  its  limitations, 
k  era  tome  try  is  of  great  value;  furthermore,  I  believe  that  phak- 
ometry,  at  least  of  the  posterior  surface,  is  worth  the  time  which 
it  requires,  in  that  it  often  affords  an  explanation  of  optical  con- 
ditions which  would  otherwise  remain  unsolved. 

The  following  authorities  have  been  consulted  in  the  prep- 
aration of  the  foregoing  chapter : 


Optometry   of   the   Refractive  Apparatus  195 

Donclers,  Anomalies  of  Refraction  and  Accommodation. 

Landolt,  Refraction  and  Accommodation  of  the  Eye. 

Scheiner,  O cuius. 

Young,  The  Mechanism  of  the  Bye. 

Holth,  Kincscopy,  Annal.  d'Oculistique,  exxviii. 

Tscherning,  Physiologic  Optics. 

Thomson,  An  Additional  Method  to  Determine  the  Degree 
of  Ametropia,  Trans.  Am.  Ophthal.  Soc,  1870. 

Hooke,  Animadversions  on  the  Machina  Coelestis  of  Johan. 
Hct'clius. 

Javal.  Note  sur  Je  Choix  des  Verres  Cylindriqucs,  Annal. 
d'  Oculistique,  1865. 

Green,  On  a  New  System  of  Tests  for  the  Det.  and  Meas. 
of  Astig.,  Trans.  Am.  Ophthal.  Soc.,  1867-1868. 

Snellen.  On  the  Methods  of  Determining  the  Acuity  of 
Vision,  Norris  and  Oliver's  System  of  Diseases  of  the  Eye. 

Snellen,  H.  Jr.,  Mydriatics  and  Myotics,  Ibid. 

Howe,  Muscles  of  the  Eye  (Cycloplegics). 

Wood,  Casey,  System  of  Ocidar  Therapeutics. 

Duane,  Refractive  Errors,  Posey's  Diseases  of  the  Eye. 

Loring.  Ophthalmoscopy. 

Bowman,  Conical  Cornea,  Royal  London  Ophthal.  Hosp.  Re- 
ports, 1859. 

Cuignet,  Kcratoscopie,  Recueil  d'ophthal.,  1873. 

Parent,  De  la  Keratoscopie,  Receuil  d'Opth.,  1880. 

Jackson,  Diseases  of  the  Eye;  and  Skiascopy. 

Priestley  Smith,  A  Simple  Ophthalmoscope  for  the  Shadou 
Test. 


CHAPTER  XI 


HYPEROPIA 


Hyperopia  (H)  is  that  condition  in  which,  when  the  ciliary 
muscle  is  in  a  state  of  relaxation,  the  retina  intersects  the  axis 
of  the  optical  system  of  the  eye  in  front  of  the  posterior  principal 
focus  of  this  system,  or  it  is  that  condition  in  which  the  antero- 
posterior diameter  of  the  eyeball  is  too  short  in  relation  to  the 
position  of  the  posterior  focus  (p.  61). 

Prior  to  the  investigations  of  Bonders  hyperopia  was  con- 
fused with  presbyopia,  and  it  was  called  hyper-presbyopia.  It 
was  thought  that  the  eyes  of  young  persons  whose  vision  was 
improved  by  convex  lenses  had  grown  prematurely  old.  It  was 
also  commonly  believed  that  it  was  very  injurious  for  such  per- 
sons to  wear  correcting  glasses.  Thus  an  immense  amount  of 
suffering  and  of  serious  injury  to  the  eyesight  was  needlessly 
endured.  We  are  therefore  greatly  indebted  to  Donders  for  the 
boon  which  he  bestowed  upon  humanity  in  the  elucidation  of  this 
subject. 

Donders  called  this  condition  of  refraction  hypermetropia* 
a  term  which  is  the  analogue  of  emmetropia.  The  word  which 
is  now  more  commonly  used,  hyperopia,  has  the  advantage  of 
being  shorter ;  it  also  corresponds  to  the  common  expression,  far- 
sightedness. 

The  hyperopic  state  of  refraction  of  itself  reveals  to  us  noth- 
ing as  regards  the  curvatures  of  the  surfaces,  the  indices  of  the 
media,  or  the  size  Of  the  eyeball.  It  indicates  only  that  there  is- 
a  disproportion  between  these  various  factors,  in  which  the  eye- 
ball is  relatively  too  short.  If  the  length  of  axis  and  the  indices 
of  the  media  approximate  closely  to  the  average  which  numerous 
investigations  have  established  as  the  standard  for  the  human 
eye,  while  the  curvature  of  one  or  more  of  the  surfaces  is  per- 
ceptibly less  than  the  average,  the  resulting  hyperopia  is  assigned 
to    deficiency   of   curvature    and    is    called    curvature-hyperopia. 

♦  From  VTTCp   uirpov     lieyond  measure,  ami  ««|»     sight. 

196 


Hyperopia  197 

When  the  curvatures  and  the  length  of  axis  are  normal,  with 
a  deviation  from  the  average  in  one  or  more  of  the  indices,  any 
resulting  hyperopia  is  called  index-hyperopia  ;  and  when  the 
curvatures  and  indices  are  normal,  the  hyperopia  is  attributable 
to  deficiency  in  length  of  axis,  and  is  called  axial  hyperopia. 

Curvature-Hyperopia 

Curvature-hyperopia  is  not  common.  Ophthalmometry 
shows  us  that  ordinarily  in  hyperopia  the  curvature  of  the  cornea 
and  of  the  lens  is  not  below  the  average,  although  exceptionally 
the  radius  of  the  cornea  may  so  much  exceed  the  standard  as 
to  produce  hyperopia  in  an  eye  of  normal  length. 

The  hyperopia  which  exists  in  aphakia,  since  it  is  due  to 
absence  of  the  lenticular  curvature,  may  be  regarded  as  curvature- 
hyperopia. 

Index-Hyperopia 

The  refractive  index  of  the  aqueous  and  vitreous  has  been 
found  so  nearly  constant  in  health  that  we  are  justified  only  under 
exceptional  circumstances  in  ascribing  hyperopia  to  abnormal 
index  of  these  media. 

If  the  density  of  these  two  media  should  be  increased,  as 
from  the  presence  of  sugar,  a  condition  of  hyperopia  would 
result,  for  the  increase  of  convergent  refraction,  which  would 
occur  at  the  cornea  would  be  overbalanced  by  the  diminution  in 
the  refraction  by  the  crystalline  lens.  In  this  way  has  been  ex- 
plained the  hyperopia  which  has  occasionally  been  observed  to 
develop  in  diabetes. 

Index-hyperopia  may  also  occur  from  the  equalization  of 
the  refractive  index  throughout  the  lens,  as  usually  takes  place 
with  increase  of  age.  As  the  density  of  the  outer  layers  of  the 
lens  approximates  that  of  the  nucleus,  the  refractive  power  is 
diminished  and  hyperopia  may  result. 

Hyperopia  due  to  the  absence  of  the  crystalline  lens,  which 
has  been  classed  as  a  curvature  defect,  may  with -equal  propriety 
be  regarded  as  index-hyperopia,  for  in  this  condition  the  total 
index  of  the  eye  is  abnormally  low. 

Axial  Hyperopia 

Occasionally  axial  hyperopia  occurs  from  pathological  dis- 
placement of  the  retina,  as  in  partial  detachment;  but  ordinarily 


198  Errors  of  Refraction 

it  is  due  to  congenital  deficiency  in  the  antero-posterior  diameter 
of  the  eye  as  compared  with  the  average  normal  diameter.  This 
is  the  typical  form  of  hyperopia,  and  to  it  we  assign  all  cases 
unless  there  is  positive  evidence  that  the  defect  is  due  to  other 
cause.  We  must  not  forget,  however,  that  in  the  lowest  grades 
of  hyperopia  this  is  an  arbitrary  distinction,  for  an  extremely 
slight  variation  in  axial  length — such  as  occurs  in  emmetropia — ■ 
will  effect  a  refractive  change  of  several  diopters,  unless  accom- 
panied by  suitable  adaptation  of  curvature  or  index. 

The  method  of  determining  the  deficiency  in  length  of  axis 
was  demonstrated  in  Part  I  (p.  80).  In  the  manner  there  de- 
scribed the  following  table  has  been  constructed,  indicating  the 
length  of  axis  and  the  deficiency  in  various  grades  of  hyperopia 
as  measured  by  the  correcting  lens  placed  at  the  anterior  focus 
of  the  eye. 

Hyperopia  Length  of  Axis         Deficiency 

oD     (Emmetropia) 23.2111111 

1  D 22.9    "  0.3  >n  111 

3D 22.2    "  1.0    " 

5D 21.5    "  1.7    " 

7D 20.9   "  2.3    " 

oD 20.2    "  3.0   " 

11D 19.5    "  3-7    " 

13  D [8.9    "  4-3    " 

15D 18.2   "  5-0   " 

From  this  table  we  see  that  a  shortening  of  1  mm  in  the 
antero-posterior  diameter  of  the  eye  corresponds  to  hyperopia  of 
3  D;  but  this  amount  of  shortening  is  by  no  means  incompatible 
with  emmetropia,  and  therefore  there  is  no  demonstrable  defi- 
ciency in  length  of  axis  in  the  lower  grades  of  hyperopia. 

If  emmetropia  is  regarded  as  the  normal  state  of  the  human 
eye.  the  axially  hyperopic  eye  must  be  regarded  as  an  eye  which 
has  not  attained  perfect  development.  In  this  respect  such  eyes 
resemble  those  of  the  lower  animals  and  of  children,  in  whom 
hyperopia  is  the  normal  condition. 

A  large  number  of  examinations  has  revealed  an  average  of 
about  3  D  of  hyperopia  in  newborn  children.  This,  however,  does 
not  correspond  to  an  antero-posterior  diameter  of  22.2  mm,  as  it 
would  in  an  adult.  The  average  length  of  axis  in  the  newborn 
is  about  17  mm,  for  the  curvature  of  the  cornea  and  of  the  crys- 
talline lens  is  greater  than  it  is  in  the  adult.  There  is  a  very- 
rapid  change  in  this  respect,  however,  and  it  is  said  that  after 


Hyperopia  199 

the  third  year  the  corneal  curvature  does  not  ordinarily  undergo 
any  material  change. 

As  age  advances  the  eye  increases,  in  size,  with  a  gradual  dim- 
inution of  hyperopia,  which  normally  passes  into  a  condition 
approximating  emmetropia  about  the  twelfth  or  fifteenth  year. 
The  proportion  of  eyes  which  reach  the  emmetropic  state  varies 
with  the  communal  habits,  since  the  eye  in  a  measure  adapts  itself 
to  the  predominating  requirements.  The  proportion  may;  fte 
approximately  estimated  as  one-half  in  adults. 

In  consequence  of  the  irritation  to  which  the  eye  is  sub- 
jected during  school  life,  and  in  some  cases  because  of  inherent 
weakness  of  the  sclera,  the  enlargement  of  the  eyeball  is  fre- 
quently not  arrested  when  emmetropia  is  attained,  and  this  fur- 
ther increase  in  the  antero-posterior  diameter  gives  rise  to  myopia. 
It  is  fortunate,  therefore,  that  this  tendency  is  counteracted  by 
the  natural  state  of  hyperopia.  ■ .       ' 

In  savage  races,  in  whom  the  influences  tending  to  cause  axial 
elongation  have  not  been  brought  into  action,  the  normal  condi- 
tion, even  in  adult  life,  is  that  of  hyperopia. 

The  eyes  of  congenitally  deaf  persons  are  also  usually  hyper- 
opia and  not  infrequently  to  a  very  high  degree.  The  cause  to 
which  is  due  the  arrest  of  development  of  the  auditory  apparatus 
affects  also  the  eye. 

Degree  of  Hyperopia 

Hyperopia  varies  in  degree  from  a  condition  imperceptibly 
differing  from  emmetropia.  on  the  one  hand,  to  microphthalmos, 
on  the  other.  In  the  former  case,  therefore,  it  is  limited  by 
the  accuracy  of  our  means  of  diagnosis.  In  the  earlier  days  of 
ophthalmology  eyes  having  hyperopia  not  exceeding  i  D  were 
regarded  as  emmetropic ;  but  now  it  is  customary  to  measure 
.25  D,  or  even  .12  D,  of  refractive  error.  In  doing  this,  how- 
ever, one  must  not  forget  that  an  eye  which  at  six  meters,  or  less, 
accepts  (without  detriment  to  vision)  a  convex  lens  not  exceed- 
ing .12  D  or  .25  D,  is  more  nearly  adapted  for  distant  vision  with- 
out the  lens  than  with  it. 

When  the  hyperopia  reaches  such  a  degree  that  the  eye  may 
be  considered  microphthalmic,  the  refractive  error  becomes  a  sec- 
ondary matter,  since  defects  in  development  of  the  media  and 
of  the  nervous  elements  usually  outweigh  in  importance  the  optica} 


2oo  Errors  of  Refraction 

defect.  Hyperopia  exceeding  14  D  or  15  D  does  not  occur  (except 
in  aphakia)  in  eyes  which  possess  useful  vision ;  in  fact,  an 
amount  exceeding  8  D  or  10  D  is  seldom  encountered. 

Low-Grade  Hyperopia. — Under  this  heading  we  include 
all  cases  of  hyperopia  in  which  the  error  is  less  than  3  D.  Eyes 
possessed  of  such  a  degree  of  hyperopia  are  in  their  anatomical 
structure  and  in  their  physiological  workings  not  inferior  to  em- 
metropic eyes  as  long  as  there  is  sufficient  accommodative  power 
to  overcome  the  refractive  error  without  undue  nervous  strain. 
Such  eyes  may,  therefore,  be  regarded  as  normal,  except  that  in 
the  process  of  growth  there  has  occurred  a  disproportion  between 
the  curvatures  and  the  length  of  axis. 

There  is,  however,  no  ground  for  the  prevalent  belief  that 
the  visual  acuity  of  far-sighted  eyes  surpasses  that  of  the  normal 
•emmetropic  eye.  It  is  true  that  the  savage  or  the  hyperopic 
frontiersman,  or  the  sailor,  may  be  able  to  distinguish  a  distant 
object  which  cannot  be  seen  by  a  town  dweller,  but  this  is  because 
the  former  has  by  familiarity  learned  to  analyze  images  which 
escape  the  attention  of  the  latter. 

Medium  Hyperopia. — This  class  embraces  those  cases 
which  are  not  less  than  3  D  and  not  more  than  5  D.  In  such 
eyes  there  is  usually  an  appreciable  deficiency  in  the  axial  length. 
This  is  rendered  apparent  by  turning  the  eye  strongly  to  the  nasal 
or  to  the  temporal  side,  when  there  will  be  revealed  an  abnormally 
great  curvature  at  the  equatorial  region  of  the  eyeball,  the  ap- 
pearance thus  differing  from  that  presented  by  the  emmetropic  or, 
to  a  still  greater  degree,  by  the  myopic  eye. 

It  is  not  only  the  eyeball  that  presents  this  characteristic 
appearance.  The  conformation  of  the  face  and  cranium  also 
frequently  exhibits  a  flattened  aspect.  The  bridge  of  the  nose, 
the  forehead,  and  the  orbital  borders  all  lack  the  relief  that  is 
present  in  more  fully  developed  skulls.  This  lack  of  development 
of  the  bones  of  the  face  occurring  with  imperfect  development  of 
the  eye  is  very  noticeable  in  certain  cases  of  asymmetry  of  the 
face,  the  eye  on  the  side  of  inferior  development  being  smaller 
than  that  on  the  other  side.  There  are,  however,  many  excep- 
tions to  this  concurrence,  for  equal  refraction  in  the  two  eyes  is 
not  uncommon  in  asymmetry  of  the  face,  and  vice  versa. 

High-Grade  Hyperopia. — This  class  embraces  all  cases 
of  hyperopia  which  exceed  5  D.     In  such  cases  the  smallness  of 


Hyperopia  201 

the  eye  is  not  confined  to  the  antero-posterior  diameter ;  the  eye 
is  noticeably  small  in  all  its  dimensions.  With  this  deficiency  in 
size  the  curvature  of  the  cornea  and  lens  is  not  infrequently 
abnormally  great.  This  type  of  eye  is  illustrated  diagram- 
matically  in  Fig.  100. 

The  imperfect  development  in  this  grade  of  hyperopia  often 
extends   to  the  nervous  mechanism — as   characterized  by  pallor 


FIG.   100 
The    Hyperopic    Eye. 

and  irregularity  of  outline  of  the  optic  disk,  or,  at  times,  by  in- 
creased redness,  simulating  neuritis.  In  such  cases  normal  visual 
acuity  is  not  attained  after  correction  of  the  refractive  error. 

Latent  and  Manifest  Hyperopia 

A  part  or  the  whole  of  the  hyperopia  of  an  eye  may  be  over- 
come by  involuntary  contraction  of  the  ciliary  muscle.  Hyperopia 
so  overcome  is  said  to  be  latent  (HI).  The  existence  of  latent 
hyperopia  can  be  ascertained  only  by  ophthalmoscopic  examina- 
tion in  a  darkened  room,  or  by  paralysis  of  the  ciliary  muscle  by 
means  of  a  cycloplegic. 

When  the  ciliary  muscle  relaxes  to  some  extent  so  that  a 
certain  portion  of  the  compensating  accommodation  may  be 
replaced  by  a  convex  lens,  the  strength  of  this  lens  represents  the 
manifest  hyperopia  (Hm).  The  sum  of  the  manifest  and  latent 
hyperopia  constitutes  the  total  hyperopia  (Ht). 

The  proportion  of  total  hyperopia  which  remains  latent  varies 
in  individuals  and  at  different  ages.  From  complete  latency  so 
often  found  in  childhood,  a  gradually  increasing  portion  becomes 
manifest  with  the  weakening  of  accommodative  power,  so  that 
in  old  age  the  total  hyperopia  is  manifest. 


202  Errors  of  Refraction 

Manifest  hyperopia  may  be  either  facultative  (Hf)  or  abso- 
lute (Ha).  A  hyperope  of  3D  may  have  normal  distant  vision 
without  any  correcting  lens ;  if  he  still  has  normal  vision  with  a 
convex  lens  of  1  D,  while  any  stronger  lens  blurs  vision  he  has 

1  D  of  manifest  and  2  D  of  latent  hyperopia.  Since  he  is  able  by 
exercise  of  his  accommodation  to  overcome  the  manifest  hyper- 
opia, the  latter  is  said  to  be  facultative.  But  when  this  same  perT 
son  is  fifty-two  or  fifty-three  years  of  age  he  has  at  his  disposal 
only  about  2  D  of  accommodation.  At  this  age  the  total  hyper- 
opia will  be  manifest,  but  only  2  D  of  this  manifest  hyperopia 
can  be  overcome  by  accommodative  action.     He  has,  therefore,. 

2  D  of  facultative  and  1  D  of  absolute  hyperopia. 

Symptoms  of  Hyperopia 

The  subjective  symptoms  of  hyperopia  vary  with  the  degree 
of  the  defect,  with  the  accommodative  power,  and  with  the  occu- 
pation and  nervous  irritability  of  the  individual.  Hence,  we  must 
not  be  surprised  to  find  slight  hyperopia  causing  very  great  annoy- 
ance in  one  person,  while  a  much  higher  degree  in  another  per- 
son may  cause  no  disturbance  whatever. 

Vision  in  Hyperopia.— As  long  as  there  is  sufficient  ac- 
commodative power  to  overcome  the  error  vision  is  unimpaired. 
Hence  in  slight  hyperopia  distant  vision  may  be  normal  until  an 
advanced  age,  and  near  vision  may  be  affected  only  in  that  read- 
ing glasses  are  required  at  a  slightly  earlier  age  than  in  emmetro- 
pia.  But  when  the  hyperopia  reaches  the  medium  degree  near 
vision  becomes  burdensome  in  early  adult  life,  and  distant  vision 
also  becomes  subnormal  before  middle  age.  Thus  a  hyperope  of 
4  D,  when  he  reaches  the  age  of  forty  years,  has  only  4.5  D  of 
accommodation,  leaving  only  .50  D  in  reserve  after  adapting  his 
eye  for  distant  vision.  He  could  not.  therefore,  maintain  normal 
distant  vision  for  more  than  a  brief  period,  and  near  work,  such 
as  reading  ordinary  print,  would  clearly  be  impossible. 

In  the  highest  grades  of  hyperopia  vision  falls  below  normal 
at  a  still  earlier  age,  and  distant  vision  may  be  defective  in  child- 
hood, even  though  there  may  be  no  arrest  of  development  of  the 
nervous  mechanism. 

Owing  to  insufficiency  of  accommodation  in  low  and  medium 
hyperopia  there  is  a  tendency  for  the  person,  as  he  grows  older, 


Hyperopia  203 

to  hold  his  book  or  other  work  at  an  abnormally  great  distance. 
On  the  other  hand,  in  the  highest  grades  of  hyperopia  distinct 
images  for  near  work  are  not  possible  even  in  childhood,  and  the 
child,  learning  this,  abandons  the  attempt  to  secure  distinctness, 
and  instead  obtains  larger  images  by  holding  his  work  very  near 
the  eyes,  thus  leading  the  casual  observer  to  the  erroneous  conclu- 
sion that  the  child  is  near-sighted. 

Defective  vision  may  also  arise  in  hyperopia  from  abnormal 
weakness  of  the  ciliary  muscle,  such  as  occurs  from  exhausting 
diseases,  or  from  paralysis  of  the  third  nerve,  as  in  diphtheria. 

Asthenopia. — This  term  is  used  to  designate  a  group  of 
symptoms  characterized  by  pain  in  and  about  the  eyes  and  in  the 
frontal  region,  extending  at  times  beyond  the  temples  and  even 
as  far  as  the  occiput  and  nape  of  the  neck.  These  disturbances 
are  produced  by  close  application  of  the  eyes,  which  tire  easily. 
After  short  use  of  the  eyes  the  print  becomes  blurred  or  unsteady, 
and  pain,  accompanied  at  times  by  photophobia,  redness  and 
watering  of  the  eyes,  becomes  so  great  that  cessation  from  work 
is  imperative.  After  a  period  of  rest  the  symptoms  disappear, 
but  upon  resumption  of  work  they  recur  with  aggravated  in- 
tensity. Asthenopia  (eyestrain  )  sometimes  gives  rise  to  nausea, 
or  to  vertigo,  and  less  commonly  to  insomnia,  mental  depression, 
nervous  prostration  (so  called),  and,  according  to  some  ophthal- 
mologists, to  chorea,  epilepsy,  and  other  reflex  disturbances. 

Asthenopia  may  result  from  any  one  of  several  causes. 

(1)  Hysterical,  nervous,  or  retinal  asthenopia  occurs  in  hys- 
terical and  neurasthenic  persons  as  a  manifestation  of  nerve-ex- 
haustion, and  it  occurs  not  infrequently  in  eyes  which  are  ap- 
parently normal. 

(2)  Muscular  asthenopia  results  from  muscular  imbalance, 
which  necessitates  an  abnormal  strain  to  preserve  binocular  vis- 
ion. Since  the  normal  relation  between  accommodation  and  con- 
vergence is  disturbed  in  hyperopia,  it  might  be  inferred  that  mus- 
cular asthenopia  would  be  a  common  symptom  in  this  affection : 
but.  since  hyperopia  is  congenital,  the  relation  between  converg- 
ence and  accommodation  may  become  adapted  to  the  hyperopic 
condition ;  in  other  cases  binocular  vision  is  abandoned  at  an 
early  age,  when  the  incentive  to  it  is  slight,  and  the  unused 
eye  passes  into  a  state  of  strabismus. 


204  Errors  of  Refraction 

(3)  Accommodative  asthenopia  results  from  overuse  of  the 
ciliary  muscle,  and  since  this  muscle  has  the  greatest  tax  thrown 
upon  it  in  the  hyperopic  state  of  refraction,  accommodative  asthe- 
nopia is  pre-eminently  the  asthenopia  of  hyperopic  eyes. 

Headache. — This  has  been  mentioned  as  being  one  of  the 
manifestations  of  asthenopia,  but  it  sometimes  occurs  without 
any  symptoms  directly  referable  to  the  eyes.  Ocular  headache 
may  consist  in  a  dull  pain  in  the  forehead,  supra-orbital  neural- 
gia, occipital  pain,  usually  combined  with  frontal  headache,  or 
severe  migraine  or  sick  headache.  Pain  at  the  vertex  is  some- 
times, though  more  rarely,  attributable  to  eye-strain. 

Objective  Symptoms. — The  characteristic  form  of  the 
face  and  of  the  eyeball  has  been  mentioned  in  the  present  chapter. 
In  addition  to  these  indications  there  are  not  infrequently  found 
marginal  blepharitis,  conjunctival  congestion  or  inflammation,  or 
epiphora,  and  sometimes,  from  prolonged  eye-strain,  congestion 
and  haziness  of  the  retina  in  the  region  of  the  optic  disk  are  ob- 
served upon  ophthalmoscopic  examination ;  but  these  symptoms 
are  not  pathognomonic.  Such  symptoms  as  may  be  so  regarded 
have  been  fully  considered  under  the  head  of  objective  methods 
of  determining  the  refractive  condition.     (Chapter  X.) 

Strabismus. — In  hyperopia  distinct  images  are  obtained 
in  near  vision  only  through  an  abnormally  great  effort  of  accom- 
modation, and  this  excess  of  accommodation  is  accompanied  by  a 
correspondingly  great  innervation  of  convergence.  If  the  desire 
for  binocular  vision  predominates,  the  excess  of  convergence  will 
be  overcome,  either  by  the  acceptance  of  blurred  images,  with  less 
accommodation,  or  by  maintaining  the  muscular  balance  at  the 
expense  of  undue  nervous  energy.  But  if  the  incentive  to  binocu- 
lar vision  is  outweighed  by  the  other  factors,  one  eye  will  be 
used  for  vision  while  the  other  assumes  a  position  of  excessive 
convergence.  This  constitutes  internal  or  convergent  strabismus. 
Hence,  anything  which  weakens  the  natural  impulse  for  binocular 
vision  facilitates  the  occurrence  of  strabismus.  This  defect  fre- 
quently appears  therefore  after  loss  or  diminution  of  sight  in  one 
eye,  or  when  one  eye  is  congenitally  defective,  or  if  the  refractive 
condition  is  unlike  in  the  two  eyes. 

The  strabismus  which  may  be  assigned  to  hyperopia  as  the 
chief  causal  factor  usually  occurs  at  an  early  age  (in  the  second 


Hyperopia  205 

or  third  year),  when  the  habit  of  binocular  vision  has  not  become 
strongly  fixed  and  when  the  secondary  image,  falling  upon  a 
peripheral  portion  of  the  retina,  seems  to  attract  no  attention. 
Sometimes  the  onset  of  the  strabismus  is  delayed  until  the 
beginning  of  school-life,  and  its  occurrence  may  be  due  to  debili- 
tating illness,  as  measles,  scarlet  fever,  or  diphtheria.  In  conse- 
quence of  the  weakness  of  accommodation  following  such  dis- 
eases, a  greater  effort  is  required  to  secure  the  proper  action  of 
the  ciliary  muscle  than  in  health,  and  this  excessive  effort  often 
produces  excessive  convergence. 

Convergent  strabismus  occurs  most  frequently  in  medium 
degrees  of  hyperopia.  In  the  lower  grades  the  relation  between 
the  two  functions  of  accommodation  and  convergence  usually 
becomes  adapted  to  the  altered  conditions,  provided  there  is  nor- 
mal incentive  to  binocular  vision.  In  the  highest  degrees  of  hyper- 
opia distinct  images  in  near  work  are  impossible,  and  the  effort  to 
secure  them  is  not  attempted.  In  such  cases  there  may  be  binoc- 
ular vision  with  indistinct  images  in  both  eyes,  or  binocular  vision 
may  be  abandoned,  the  work  being  brought  very  near  the  eye  for 
the  sake  of  enlarged  images.  In  the  latter  case,  since  there  is  no 
attempt  to  form  distinct  images  with  the  aid  of  accommodation, 
there  is  no  incentive  to  convergence,  and  the  unused  eye  may  fall 
into  a  state  of  divergence.  In  this  way  is  produced  the  divergent 
strabismus  which  sometimes  occurs  in  high  degrees  of  hyperopia. 

The  foregoing  explanation  of  the  causal  relation  between  hy- 
peropia and  convergent  strabismus  was  given  by  Bonders,  but  he 
erred  in  believing  that  hyperopia  was  the  most  important  factor 
in  the  etiology  of  the  strabismus.  Many  recent  authorities  go  too 
far  the  other  way  and  hold  that  hyperopia  has  no  etiological  con- 
nection with  strabismus.  While  a  deficiency  in  the  normal  im- 
pulse for  binocular  vision  is  doubtless  the  most  potent  factor,  the 
presence  of  hyperopia  acts  as  a  very  powerful  predisposing  cause 
of  strabismus,  and  the  correction  of  this  defect  often  enables  the 
eyes  to  assume  their  normal  function  of  binocular  vision. 

Diagnosis  of  Hyperopia 

Hyperopia  may  be  suspected  from  the  presence  of  some  or 
all  of  the  above-mentioned  symptoms,  but  its  existence  is  dem- 
onstrated and  its  degree  measured  by  means  of  the  subjective  and 


2p6  Errors  of  Refraction 

objective  tests  considered  in  Chapter  X.  In  the  routine  examina- 
tion for  the  determination  of  refractive  error  the  objective  ex- 
amination is  usually  conducted  first  (or  after  a  short  preliminary 
subjective  examination)  beginning  with  ophthalmometry.  Oplv 
thalmometry  is  useful  in  hyperopia  only  in  so  far  as  it  reveals 
the  coexistence  or  absence  of  astigmia.  i 

After  completion  of  the  ophthalmometry  examination  skia- 
scopy is  next  in  order.  The  indications  for  the  employment  of  a 
cycloplegic  in  this  test  are  the  same  as  in  the  subjective  examina- 
tion with  trial  lenses. 

Owing  to  the  greater  accuracy  of  skiascopy,  ophthalmo- 
scopy is  no  longer  used  in  the  final  measurement  of  refractive 
error,  but  it  is  valuable  in  that  it  enables  the  examiner  to  note  the 
condition  of  the  media  and  of  the  fundus. 

In  strabismus  and  in  high  hyperopia  it  is  often  necessary  to 
correct  the  error  before  the  child  is  old  enough  to  submit  to  the 
subjective  examination.  In  such  cases  reliance  must  be  placed 
upon  ophthalmoscopy  and  skiascopy  with  cycloplegia. 

After  the  completion  of  the  objective  examination  the  sub1 
jective  test  with  trial  lenses  is  undertaken. 

In  regard  to  the  advisability  of  using  a  cycloplegic  for  the 
determination  of  hyperopia  ophthalmologists  are  not  all  of  the 
same  opinion.  Some  believe  that  latent  hyperopia  does  not  re- 
quire correction,  and  that  by  exercise  of  proper  care,  as  by  the 
fogging  method,  all  of  the  relaxable  accommodation  may  be  dis- 
covered without  the  use  of  any  drug.  I  believe  that  without  re- 
sorting to  cycloplegia  the  experienced  refractionist  may  in  quite 
a  large  proportion  of  young  persons  prescribe  glasses  which  will 
bring  relief  from  asthenopia.  There  is,  however,  always  an  uncer- 
tainty as  to  the  amount  of  latent  error;  and  not  infrequently  the 
strength  of  the  glasses  must  be  increased  at  short  intervals  tc 
keep  pace  with  the  continual  increase  of  the  manifest  error. 

The  employment  of  a  cycloplegic  has,  therefore,  the  great 
advantage  of  enabling  us  to  derive  certain  knowledge  of  the  true 
static  refraction  and  of  the  behavior  of  the  ciliary  muscle.  On 
this  account  it  is  better  to  paralyze  the  accommodation  before  at- 
tempting to  make  an  accurate  estimate  of  the  refractive  error  of  a 
child  or  young  adult. 

,        As  the  age  of  the  patient  increases  the  necessity  of  using  a 


Hyperopia  207 

■cycloplegic  becomes  less  imperative.  In  my  opinion  it  is  not,  as 
a  rule,  required  after  the  age  of  thirty  years.  Its  use  may,  under 
favorable  conditions,  be  dispensed  with  prior  to  this  age,  and  it 
may  in  other  cases  be  required  at  a  greater  age.  In  the  choice  of 
a  cycloplegic  the  tendency  among  ophthalmologists  is  more  and 
more  to  rely  upon  homatropin  in  ordinary  routine  work,  and  tp 
reserve  the  long-persisting  cycloplegics,  such  as  atropin,  for  cases 
•of  strabismus  and  spasm  of  the  accommodation. 

When  a  cycloplegic  is  used  the  eyes  should  be  protected 
from  an  excess  of  light  by  dark  or  amber-tinted  glasses  until  the 
mydriasis  disappears. 

After  the  age  of  forty  years  a  cycloplegic  should  not  be 
used  until  it  has  been  ascertained  that  the  patient  has  no  tendency 
to  glaucoma,  as  disastrous  results  have  occurred  from  lack  of  this 
precaution. 

Treatment  of  Hyperopia 

The  degree  of  hyperopia  having  been  ascertained,  in  accord- 
ance with  the  preceding  directions,  it  is  our  duty  to  prescribe  such 
lenses  as  will  afford  the  eyes,  if  possible,  their  normal  or  physio- 
logical working  power. 

While  some  ophthalmologists  maintain  that  latent  hyperopia 
does  not  require  correction,  others  believe  that  the  eyes  should 
in  every  case  be  placed  in  a  condition  of  emmetropia  by  means  of 
lenses  which  correct  any  deviation  from  this  ideal  condition. 
Neither  of  these  plans  should  be  blindly  followed.  It  is  impos- 
sible, to  formulate  a  general  rule,  for  each  case  must  be 
judged  in  accordance  with  the  symptoms  and  attendant  circum- 
stances. While  the  measurement  of  refractive  error  is  in  most 
cases  a  simple  procedure,  the  prescribing  of  proper  lenses  is  a 
far  more  difficult  matter,  which  requires  much  thought  and  care. 
All  that  may  profitably  be  formulated  is  an  outline  of  the  method 
usually  to  be  pursued ;  we  must  leave  to  the  judgment  of  the 
reader  the  modifications  to  be  made  in  practical  work. 

Correction  of  Low-Grade  Hyperopia  in  Childhood. — 

It  is  not  probable  that  hyperopia  of  .50  D  or  .75  D  is 
capable  of  causing  asthenopia  or  other  disturbance  in  a  healthy 
child  who  has  at  his  disposal  10  D  or  12  D  of  accommodation. 
In  those  children  in  whom  the  correction  of  so  'slight  an  error 


208  Errors  of  Refraction 

brings  relief,  it  is  likely  that  the  beneficial  result  is  due  to  psychic 
influence,  and  not  to  the  aid  which  the  lenses  give  to  the  accom- 
modation. That  many  children  desire  to  wear  glasses  for  egotis- 
tical reasons  is  unquestionable.  But  since  such  influences  are  not 
unimportant  in  the  production  of  subjective  symptoms,  it  may 
perhaps  occasionally  be  proper  to  prescribe  weak  lenses  in  cases 
of  this  kind,  with  the  instruction  that  they  are  to  be  worn  only 
for  near  work,  and  with  the  statement  also,  in  the  presence  of  the 
child,  that  a  cure  will  be  effected  in  a  short  time.  In  almost  all 
these  cases  the  symptoms  will  be  relieved  and  the  glasses  discard- 
ed in  the  course  of  a  few  months. 

On  the  other  hand,  it  must  be  borne  in  mind  that  while  hyper- 
opia is  the  natural  condition  in  childhood,  the  school-life  of  the 
child  of  modern  civilization  is  artificial,  and  it  may  well  be  that 
the  accommodation  which  is  ample  for  a  life  in  accordance  with 
nature  is  insufficient,  even  in  a  moderate  degree  of  hyperopia,  to 
stand  the  strain  of  near  work  entailed  by  school  duties.  In  such 
cases  glasses  should  be  ordered  for  school  use  and  for  reading. 
A  portion  only  of  the  hyperopia  should  be  corrected,  because  total 
correction  would  entail  defective  distant  vision, — a  manifest  dis- 
advantage in  school  work.  As  a  rule,  not  more  than  one-half  or 
two-thirds  of  the  total  correction  can  be  comfortably  worn  before 
the  age  of  fifteen  years. 

Correction  of  Low-Grade  Hyperopia  in  Adult  Life. — 

Low-grade  hyperopia  which  has  passed  unnoticed  in  childhood 
requires  correction  sooner  or  later  in  the  adult.  The  age  at 
which  correction  becomes  necessary  varies  with  the  amount  of 
error  and  with  the  health  and  occupation  of  the  individual.  As  a 
rule,  relief  will  be  sought  early  by  accountants  and  others  en- 
gaged in  exacting  near  work.  If  the  hyperopia  is  latent,  and 
especially  if  it  is  slight  (not  more  than  I  D),  the  use  of  glasses 
in  near  work  will  ordinarily  suffice.  On  the  other  hand,  manifest 
hyperopia  is  an  indication  for  the  constant  use  of  glasses.  In  some 
cases,  however,  and  especially  in  elderly  persons  who  are  not  en- 
gaged in  exacting  work,  correction  for  near  use  only  is  required. 

When  correction  of  the  manifest  error,  required  for  con- 
stant wear,  is  insufficient  for  near  work,  it  may  be  necessary 
to  order  two  pairs  of  glasses,  the  manifest  correction  for  distance, 
and  the  total  correction  for  near  work ;  but  ordinarily  a  judicious 


Hyperopia  209 

selection  of  a  single  pair  for  all  purposes  will  afford  relief  until 
the  onset  of  presbyopia. 

Correction  of  Medium  and  High-Grade  Hyperopia. — 

A  medium  grade  of  hyperopia  may  pass  unnoticed  through- 
out childhood ;  but  usually,  and  especially  in  town  life,  it  will  give 
rise  to  asthenopia  early  in  the  school  career.  In  the  correction  of 
hyperopia  reaching  a  medium  degree  glasses  must  be  worn  con- 
stantly, as  a  rule,  even  in  childhood,  for  the  proper  relaxation  of 
the  ciliary  muscle  can  be  obtained  only  by  prolonged  training  with 
the  use  of  the  correcting  lenses ;  moreover,  a  fixed  relation  be- 
tween accommodation  and  convergence  cannot  be  established  un- 
less the  glasses  are  worn  constantly.  The  proportion  of  the 
hyperopia  to  be  corrected  varies  with  the  age  and  with  other 
circumstances,  in  accordance  with  which  the  examiner  must  judge 
as  to  the  proper  lenses  to  be  prescribed. 

Similarly,  high-grade  hyperopia  requires  correction  at  an 
early  age — at  or  before  the  beginning  of  the  school  career. 

Treatment  of  Muscular  Disturbances. — Muscular  as- 
thenopia or  strabismus,  in  so  far  as  either  of  these  affections 
may  be  directly  due  to  hyperopia,  requires  only  the  treatment  ap- 
propriate for  the  causal  refractive  error;  but  the  concurrence  of 
muscular  disturbance  is  a  factor  which  must  be  considered  in 
the  prescription  of  correcting  lenses.  Even  in  mild  hyperopia,  in 
which  during  childhood  correction  for  near  work  might  otherwise 
suffice,  it  would  be  imperative  that  glasses  should  be  worn  con- 
stantly if  the  hyperopia  should  be  complicated  by  strabismus; 
furthermore,  it  would  not  be  advisable,  as  previously  recom- 
mended, to  leave  any  considerable  part  of  the  latent  hyperopia  un- 
corrected. 

Whereas  in  uncomplicated  hyperopia  correction  is  not  often 
called  for  before  the  school  age,  the  occurrence  of  strabismus  re- 
quires correction  of  the  hyperopia  at  the  earliest  age  compatible 
with  the  wearing  of  glasses — usually  between  the  second  and 
third  year. 

When  muscular  disturbance  which,  may  have  been  originally 
produced  by  hyperopia  has  become  so  fixed  through  neglect  that 
correction  of  the  hyperopia  does  not  restore  the  proper  muscular 
balance,  resort  must  then  be  had  to  other  measures.  These  will 
be  considered  in  a  subsequent  chapter. 


2io  Errors  of  Refraction 

Secondary  Effects  of  Convex  Lenses 

In  the  application  of  lenses  to  the  correction  of  hyperopia, 
there  are  certain  secondary  effects  which  not  infrequently  create 
confusion  until  the  eyes  become  accustomed  to  the  altered  con- 
ditions. 

Enlargement  of  the  Retinal  Image. — We  have  learned 
in  Part  I  (p.  79)  that  the  retinal  image  in  unaided  axial  hyper- 
opia is  slightly  smaller  than  in  emmetropia ;  that  the  correcting 
lens  exerts  a  magnifying  effect  upon  this  image,  such  that  if  the 
lens  is  placed  at  the  anterior  focus  of  the  eye,  the  resulting 
image  is  of  the  same  size  as  that  of  the  emmetropic  eye;  and 
that  if  the  lens  is  farther  from  the  eye  than  the  anterior  focus, 
the  image  is  larger  than  that  of  the  emmetropic  eye.  Since 
spectacle-lenses  are  usually  of  low  power  as  compared  with  the 
refractive  action  of  the  eye,  and  since,  although  worn  without 
the  anterior  focus,  they  are  yet  very  near  this  point,  the  retinal 
image  in  corrected  axial  hyperopia  does  not  materially  differ  from 
that  in  emmetropia.  Hence,  when  a  hyperope  replaces  his  over- 
strained accommodation  by  convex  lenses  his  retinal  images  are 
slightly  larger  than  those  to  which  he  has  been  accustomed. 

In  the  curvature-hyperopia  of  aphakia  the  correcting  lens  is 
placed  within  the  anterior  focus  of  the  aphakic  eye,  and  the  effect 
of  the  lens  is  to  reduce  the  size  of  images,  yet  they  are  materially 
larger  than  in  emmetropia  and,  consequently,  larger  than  they 
were  before  removal  of  the  crystalline  lens. 

Apparent  Magnification  of  Objects. — Of  greater  im- 
portance than  the  actual  change  in  the  retinal  image  is  the  ap- 
parent enlargement  produced  by  convex  lenses — an  effect  which 
is  due  entirely  to  psychic  influence.  No  knowledge  as  to  the  size 
of  an  object  is  revealed  by  the  size  of  the  retinal  image  alone.  It 
is  the  size  of  this  image  taken  in  conjunction  with  the  estimated 
distance  by  which  we  form  a  correct  judgment  as  to  the  dimen- 
sions of  an  object. 

The  estimation  of  distance  and  size  is  a  complex  mental  act, 
based  upon  previous  experience  and  association  of  muscular  ac- 
tions. In  this  act  the  degree  of  accommodation  and  convergence 
exercised,  the  movements  of  the  eyes  required  to  fix  every  part  of 
the  object,  and  the  knowledge  as  to  the  actual  size  of  the  object 
are  all  important  contributing  factors. 


Hyperopia  211 

Convex  lenses,  by  diminishing  the  amount  of  accommodation 
required  to  see  an  object  distinctly,  lead  one  to  suppose  that  the 
object  is  more  remote  than  it  actually  is,  and,  consequently,  they 
make  the  object  appear  larger  than  it  is  as  seen  with  the  naked 
eye.  On  this  account  objects  usually  appear  abnormally  large  to 
the  hyperope  when  he  begins  to  wear  correcting  lenses,  even 
though  the  actual  enlargement  of  the  retinal  images  may  be  neg- 
ligible. 

Alteration  in  the  Relation  between  Convergence  and 
Accommodation. — In  uncomplicated  hyperopia  a  certain  con- 
vergence is  accompanied  by  a  greater  amount  of  accommodation 
than  in  emmetropia ;  hence,  when  correcting  lenses  are  worn  the 
associated  nerve  centers  must  be  trained  to  modify  this  relation 
so  that  it  will  conform  to  the  emmetropic  standard.  This  is  a 
common  cause  of  disturbance  when  glasses  are  first  worn. 

When,  on  the  other  hand,  hyperopia  is  accompanied  by  ex- 
cessive convergence,  the  restoration  of  the  normal  relation  between 
convergence  and  accommodation  is  one  of  the  benefits  bestowed 
by  the  correcting  lenses. 

Prismatic  Action  of  Convex  Lenses. — When  the  optical 
center  of  a  lens  lies  in  the  line  of  vision  the  object  seen 
undergoes  no  lateral  displacement;  but  when  an  object  is  viewed 
through  an  eccentric  portion  of  a  lens  the  object  will  appear  dis- 
placed towards  the  thinnest  part  of  the  lens,  just  as  towards  the 
apex  of  a  prism ;  that  is,  in  the  case  of  a  convex  lens  the  object 
will  be  displaced  away  from  the  center  of  the  lens.  Hence,  when 
convex  lenses  are  so  adjusted  that  their  centers  lie  without  the 
lines  of  vision  of  the  two  eyes,  any  object  viewed  will  be  displaced 
towards  the  nasal  side,  and  consequently,  in  order  that  the  image 
may  fall  upon  the  macula  each  eye  must  be  rotated  towards  the 
nose  to  a  greater  degree  than  when  the  object  is  viewed  without 
the  lenses.  In  other  words,  the  lenses  require  an  increase  of  con- 
vergence, and  the  object  seems  nearer  than  it  does  with  the  unaid- 
ed eye. 

On  the  other  hand,  if  the  centers  of  the  lenses  are  within 
the  lines  of  vision,  the  lenses  are  comparable  to  prisms  having 
their  bases  towards  the  nose,  and  convergence  is  diminished  by 
their  use. 

The  prismatic  action  of  weak  lenses  is  slight,  but  in  lenses 
of  high  power,  and  especially  in  those  required  after  the  removal 


212  Errors  of  Refraction 

of  cataract,  the  disturbance  arising  from  this  action  is  some- 
times so  great  as  seriously  to  interfere  with  the  comfort  of  wear- 
ing such  glasses. 

Prescription  of  Lenses. — The  refractionist  determines 
the  power  of  the  lenses  which  he  desires  his  patient  to  wear,  but 
if  a  competent  optician  is  available,  it  is  better  to  leave  to  him 
the  adjustment  and  adaptation  of  these  lenses  in  suitable  frames. 
The  refractionist  must,  however,  be  familiar  with  the  various 
kinds  of  frames  and  lenses  which  can  be  supplied,  in  order  that 
he  may  be  able  to  assist  his  patient  in  procuring  the  most  advan- 
tageous adjustment.  He  must  also  be  able  to  judge  as  to  the 
accuracy  with  which  the  optician  has  performed  his  work. 

In  an  order  or  prescription  for  glasses  the  lens  which  is  pre- 
scribed for  each  eye  is  indicated  by  the  letter  R  (right)  or  L 
(left)  as, 

R  -f-  2.50  D,  sph. 
L  +  2.25  D,  sph. 

Instead  of  the  designations  right  and  left  we  may  write  the 
Latin  equivalents,  O  D  (oculus  dexter),  and  0  S  (oculus  sinis- 
ter). 

We  must  signify  whether  the  glasses  are  for  constant  use  or 
only  for  near  work  and,  for  the  purpose  of  identification,  we 
must  write  the  patient's  name  and  the  date  of  the  order.  We 
may  also,  if  we  deem  it  advisable,  specify  the  character  of  mount- 
ings to  be  used — whether  "eye-glasses"  or  spectacles,  frames  or 
rimless.  In  filling  the  foregoing  prescription  the  optician  would 
decide  whether  he  would  supply  biconvex  or  periscopic  lenses. 
He  would  also  be  free  to  use  his  own  judgment  as  to  the  size  of 
the  glass  to  be  selected. 

The  periscopic  convex  lens,  as  commonly  supplied,  has  a  concave 
curvature  of  —  1.25  D  (that  is,  the  curvature  of  a  plano-concave  lens  of 
1.25  D)  on  the  side  next  to  the  eye  with  a  suitable  convex  curvature  on 
the  other  side.  This  is  the  form  which  would  be  furnished  by  the  optician 
in  filling  an  order  for  periscopic  lenses.  If  a  greater  periscopic  effect  is 
desired,  the  appropriate  concavity  should  be  prescribed.  Percival  and 
Ostwah  have  deduced  from  calculation  the  form  of  curvature  best  adapted 
for  extensive  field  of  vision  in  various  grades  of  lenses.  Lenses  may  be 
ordered  in  accordance  with  these  deductions,  but  for  ordinary  use  the 
simpler  forms  suffice. 

The  size  of  the  lens — or  the  eye,  as  it  is  technically  called — 
is  indicated  by  its  number.    No.  1  (37x28  mm)  is  generally  used 


Hyperopia  213 

for  children,  though  a  smaller  size,  No.  2,  is  sometimes  desirable 
for  very  young  children.  No.  o  (39x30  mm)  may  be  ordered  for 
adolescents  and  small-faced  adults.  Nos.  00  (40x32  mm)  and 
000  (41x33  mm)  are  the  sizes  more  commonly  used  for  adults. 
For  special  purposes  even  larger  sizes,  0000  and  jumbo,  may  be 
advantageous. 

Verification  and  Adjustment  of  Lenses. — We  should 
verify  the  lenses  which  we  have  prescribed,  and  their  adjustment, 
and  for  this  purpose  we  should  instruct  our  patient  to  return  to 
us  after  procuring  the  glasses  from  the  optician. 

The  method  of  verification  has  been  described  in  a  previous 
chapter.  As  to  the  adjustment  of  the  lenses  in  suitable  mountings, 
the  glasses  should  be  as  near  as  possible  to  the  eyes  without  touch- 
ing the  lashes,  and  the  optical  center  of  each  lens  should  lie 
slightly  to  the  inner  side  of  the  line  of  distant  vision.  If  the 
glasses  are  for  near  use  only,  they  should  be  dropped  5  mm,  or 
6  mm,  tipped  forward  150,  and  the  center  of  each  glass  should  be 
carried  in  towards  the  nose  3  mm  (Duane). 

The  following  authorities  have  been  consulted  in  the  prepara- 
tion of  the  foregoing  chapter : 

Cooper,  Practical  Remarks  on  Near  Sight,  Aged  Sight  and 
Impaired  Vision  (1849). 

Donders,  Anomalies  of  Refraction  and  Accommodation. 

Knapp,  Die  Kriimmung  der  Hornhaut  des  menschlichen 
Auges. 

Helmholtz,  Optique  Physiologique. 

Schiotz,  Untersuchungen  von  969  Augen,  Arch,  fur  Augen- 
heil.     1885. 

Landolt,  Refraction  and  Accommodation  of  the  Eye. 

Baker,  Anatomy  of  the  Eyeball,  Norris  and  Oliver's  System 
of  Diseases  of  the  Eye. 

Duane,  Refractive  Errors,  Posey's  Diseases  of  the  Eye. 

Percival,  Periscopic  Lenses,  Archives  of  Ophthalmology,  1901. 

Ostwalt,  Remarks  upon  Periscopic  Lenses,  Ibid.,  1902. 

Worth,  Etiology  and  Treatment  of  Squint. 

Schirmer,  Contribution  a  I'Histoire  de  I'Astigmatisme  et  de 
I'Hypermetropie,  Annal.  d'Oculistique,  1869. 


CHAPTER  XII 


MYOPIA 


Myopia  (M)  is,  as  previously  defined,  that  condition  in 
which  the  retina  lies  behind  the  posterior  principal  focus  of  the 
eye  when  the  ciliary  muscle  is  relaxed ;  or  it  is  that  condition  in 
which  the  eye  is  too  long  relatively  to  the  principal  focal  distance. 

The  word  myopia*  originally  indicated  the  practice  of  look- 
ing at  objects  through  the  partly  closed  lids,  whereby  the  blurring 
of  images  is  diminished ;  but  as  this  habit  is  common  in  other 
conditions  also,  the  expression  is  not,  from  a  scientific  point  of 
view,  without  fault.  Donders  therefore  proposed  the  word  brachy- 
mctropia.f  as  corresponding  with  emmetropia  and  hypermetropia. 
But  myopia  is  shorter  and  more  euphonious  than  any  of  its  pro- 
posed substitutes ;  moreover,  it  has  the  sanction  of  very  long 
usage,  since  it  dates  from  the  time  of  Aristotle.  It  is  therefore 
appropriate  that  its  place  should  be  retained  in  our  ophthalmologi- 
cal  terminology. 

The  expressions  near-sightedness  and  short-sightedness  are 
also  commonly  used  in  reference  to  this  condition  of  refraction. 

Curvature-Myopia 

Ophthalmometry  examinations  have  not  shown  any  general 
excess  of  curvature,  either  of  the  cornea  or  lens,  in  myopia.  Ex- 
ceptionally, however,  myopia  is  due  to  excessive  curvature,  as  in 
keratoconus  or  conical  cornea,  in  lenticonus,  and  in  subluxation 
of  the  crystalline  lens. 

In  keratoconus  the  curvature  of  the  cornea  at  its  apex  is  so 
great  as  to  give  rise  to  a  high  degree  of  myopia  (Fig.  101).  On 
the  other  hand,  the  flattening  at  the  periphery  of  the  cornea  gives 
rise  to  hyperopia  for  those  rays  which  pass  through  this  part  of  the 
cornea.  On  this  account  when  the  pupil  is  large  the  vision  may 
be  better  with  a  convex  lens  which  corrects  the  peripheral  rays 
than  with  a  concave  lens  which  corrects  the  central  rays. 

*  From  p-xitiv    to  shut,  to  blink,  and  »»|»,  sight,  eye. 

t  From  Ppa\v  p,«Vpov,  short  measure,  and  om|»,  sight,  eye. 

214 


Myopia  215 

Lenticonus  is  a  very  rare  condition.  Myopia  from  excessive 
curvature  of  the  lens  is  more  likely  to  be  the  result  of  subluxation, 
the  lens  being  relieved  from  traction  of  the  ciliary  ligament,  while 
it  remains  in  the  pupillary  area. 


FIG.     IOI 
Keratoconus 


A  few  cases  have  been  recorded  in  which  there  has  been  a 
sudden  occurrence  of  hyperopia  in  diabetes,  the  probable  explan- 
ation of  which  was  given  in  the  last  chapter;  more  frequently, 
however,  it  has  been  observed  in  this  disease  that  eyes  which 
were  previously  emmetropic  or  hyperopic  have  become  myopic. 
It  is  probable  that  this  condition  results  from  a  curvature  change, 
and  that  it  is  due  to  swelling  of  the  crvstalline  lens. 


'& 


Index  Myopia 

The  only  condition  which,  as  far  as  we  know,  may 
give  rise  to  index-myopia  is  an  increase  in  the  refractive 
index  of  the  lens,  such  as  sometimes  occurs  in  old  age,  especially 
in  the  early  stage  of  senile  cataract.  This  increase  of  index  may 
be  due  to  an  increase  of  density  of  the  nucleus  without  a  cor- 
responding increase  of  density  in  the  cortical  part  of  the  lens,  or 
to  an  increase  of  nuclear  curvature  resulting  from  the  swelling 
of  the  degenerating  fibers.  Since  glasses  which  have  previously 
been  worn  for  the  correction  of  presbyopia  may  no  longer  be 
required,  the  individual  rejoices  in  the  so-called  second  sight — 
at  the  expense,  however,  of  distant  vision,  which  becomes  de- 
fective from  the  myopic  state  of  refraction.  This  condition  is 
usually  temporary,  being  succeeded  by  declining  vision  as  the 
result  of  opaqueness  of  the  lens. 

Axial  Myopia 

Myopia  is  ordinarily  due  to  excessive  length  of  the 
antero-posterior  diameter  of  the  eye.  Excessive  length  as 
a  factor  in  the  etiology  of  myopia  was  dwelt  upon  by  Beer  ( 1792), 


2i6  Errors  of  Refraction 

but  it  was  through  the  demonstrations  and  publications  of  Arlt 
(1854)  that  the  relation  between  axial  elongation  and  myopia 
became  generally  understood. 

The  following  table,  constructed  in  accordance  with  the 
method  previously  described  (p.  80),  indicates  the  theoretical 
length  of  axis  in  various  grades  of  myopia,  as  measured  by  the 
correcting  lens  placed  at  the  anterior  focus  of  the  eye. 

Myopia  Length  of  Axis        Excess 

oD     (Emmetropia) 23.2  mm. 

iD 23.5  "  0.3  mm 

3D 24.2  "  1.0  " 

5D 24.9  "  1.7  " 

7D 25.5  "  2.3  '* 

oD 26.2  "  3.0  " 

11  D 26.9  "  3-7  " 

13  D 27.5  "  4-3  " 

15  D 28.2  "  5.0  " 

'  17D 28.9  "  5-7  " 

19  D 29.5  "  6.3  " 

21  D 30.2  "  7.0  " 

23  D 30.9  "  7-7  " 

25  D 31.5  "  8.3  " 

30  D 33.2  "  10.0  " 

We  see  from  this  table  that  the  axial  length  in  myopia  of 
3  D  is  24.2  mm.  If  1  mm  is  allowed  for  the  thickness  of  the 
choroid  and  sclera,  the  antero-posterior  diameter  of  the  eye  in 
this  degree  of  myopia  is  25.2  mm.  But  an  axial  length  of  25  mm 
is  not  incompatible  with  emmetropia.  Hence,  in  low  degrees  of 
myopia  the  size  and  shape  of  the  eyeball  differ  imperceptibly,  or 
at  most  but  slightly,  from  the  normal  condition.  In  high  myopia, 
on  the  other  hand,  and  especially  in  that  exceeding  10  D,  the 
elongation  is  so  great  as  to  effect  a  pronounced  change  in  the 
form  of  the  eye. 

As  hyperopia  is  regarded  as  an  imperfectly  developed  con- 
dition, so  it  might  seem  that  the  myopic  eye  has  undergone  exces- 
sive development.  Since  hyperopia  is  the  normal  type  in  the 
lower  animals  and  in  savages,  there  can  be  no  doubt  that  the  work 
to  which  the  eyes  are  subjected  by  the  requirements  of  civilization 
promotes  an  increased  growth  of  these  organs.  Furthermore,  it 
would  be  unreasonable  to  suppose  that  in  this  process,  which  oc- 
curs in  conformity  to  the  law  of  adaptation  to  use,  a  develop- 
ment which  frequently  stops  short  of  emmetropia  should  never 
exceed  this  limit.  It  must  be  admitted,  therefore,  that  low  myo- 
pia may  be  due  to  physiological  overgrowth  of  the  eye.    Yet  in  the 


Myopia  217 

vast  majority  of  cases  the  excessive  length  arises,  not  from  over- 
growth, but  from  stretching  or  distention  of  the  ocular  coats. 
When  the  myopia  does  not  exceed  a  moderate  degree,  the  stretch- 
ing is  so  slight  that  anatomical  examination  frequently  affords  no 
positive  evidence  of  its  existence;  but  the  fact  that  it  is  a  process 
of  stretching  and  not  of  growth  is  revealed  by  the  clinical  progress 
of  axial  myopia,  by  the  increase  under  the  strain  of  near  work, 
under  unhygienic  conditions,  and  by  the  arrest  of  the  process  when 
these  factors  are  removed. 

Theories  as  to  the  Origin  of  Axial  Myopia 

While  it  is  well  established  that  the  prolonged  use  of  the  eyes 
in  near  work  is  conducive  to  the  formation  of  myopia,  the  means 
by  which  the  enlargement  of  the  eye  is  effected  has  given  rise  to 
much  discussion.  The  various  hypotheses  which  have  been  offered 
in  explanation  of  the  occurrence  of  axial  elongation  are  divisible 
into  two  general  classes.  The  first  class  embraces  those 
hypotheses  which  attribute  the  deleterious  effect  of  near  work  to 
the  prolonged  exercise  of  accommodation,  while  in  the  hypotheses 
of  the  second  class  convergence  is  regarded  as  the  causal  factor. 

Coccius  and  Hjort  were  led  to  believe  from  their  experi- 
ments that  the  intra-ocular  pressure  was  increased  during  accom- 
modation, and  this  supposition  gave  rise  to  the  opinion,  widely  ac- 
cepted, that  distention  of  the  sclera  was  due  to  the  long  continu- 
ance of  this  abnormal  pressure.  This  hypothesis  lacks  confirma- 
tion, since  it  has  never  been  proved  that  intra-ocular  pressure  is 
actually  increased  by  accommodative  action.  On  the  other  hand, 
experiments  made  by  Hess  and  Heine  indicate  that  accommoda- 
tion does  not  cause  any  increase  of  pressure. 

According  to  another  theory,  accommodation  is  injurious, 
not  so  much  from  increase  of  pressure,  as  from  the  traction  which 
is  exerted  upon  the  choroid  with  consequent  inflammatory  changes 
followed  by  atrophy  and  thinning  of  the  choroid  and  sclera.  This 
hypothesis  has  as  its  basis  the  experiments  of  Hcnsen  and  Voelck- 
crs,  who  demonstrated  a  forward  movement  of  the  choroid  dur- 
ing contraction  of  the  ciliary  muscle.  There  is,  however,  no  valid 
reason  for  the  assumption  that  this  physiological  movement  gives 
rise  to  inflammation.  Furthermore,  the  experiments  of  Hess  and 
Heine  show  that  it  is  only  the  anterior  portion  of  the  choroid 


218  Errors  of  Refraction 

which  participates  in  this  movement,  while  the  posterior  portion 
alone  is  concerned  in  the  development  of  myopia. 

Those  who  hold  accommodation  responsible  for  the  produc- 
tion of  myopia,  assign  much  importance  to  spasm  of  the  ciliary 
muscle.  But  this  is  present  in  many  young  persons  who  never 
become  myopic,  nor  is  it  more  common  in  myopic  than  in 
other  eyes. 

A  potent  argument  against  the  accommodation  theory  lies  in 
the  fact  that  there  is  no  general  tendency  to  increase  of  refraction 
(diminution  of  the  hyperopia)  in  those  eyes  upon  which  the 
greatest  accommodative  tax  is  thrown,  that  is,  in  the  higher  grades 
of  hyperopia. 

The  influence  of  convergence  upon  the  form  of  the  eyeball 
is  doubtless  of  greater  import  than  that  of  accommodation.  When 
the  internal  recti  are  strongly  contracted,  the  external  recti  bind 
closely  about  the  outer  halves  of  the  eyeballs,  and  at  the  same 
time  the  two  oblique  muscles  increase  their  traction  in  order  to 
prevent  the  globes  from  sinking  backward  into  the  orbits.  The 
pressure  upon  the  eyes. is  thereby  increased,  and  a  direct  traction 
(stretching)  is  made  upon  the  posterior  polar  region  of  the  sclera 
by  the  oblique  muscles. 

Arlt  advanced  the  theory  that  convergence  was  harmful  also 
from  compression  of  the  posterior  ciliary  vessels  by  the  external 
recti  and  inferior  oblique  muscles  with  resultant  venous  stasis  and 
choroidal  inflammation.  Fuchs  also  claims,  in  corroboration  of 
this  theory,  that  the  position  of  one  of  the  venae  vorticosae  is 
such  that  it  must  suffer  compression  by  the  inferior  oblique  in 
convergence. 

The  influences  which  have  been  so  far  considered  are  such 
as  are  common  to  all  who  are  engaged  in  exacting  near  work  (eye 
workers)  ;  but  since  only  a  certain  proportion  (about  25  per  cent 
in  this  country  and  about  50  per  cent  in  Germany)  of  eye  workers 
become  myopic,  it  is  necessary  to  assume  the  existence  of  pre- 
disposing causes  in  those  eyes  which  become  subject  to  elonga- 
tion. 

First,  there  arises  the  question  as  to  the  influence  of  the  form 
of  the  skull  upon  the  length  of  the  eye.  The  largeness  of  the  eyes 
and  the  great  interpupillary  distance  which  exists  in  highly-devel- 
oped crania,  render  convergence  more  difficult  of  accomplishment 
than  in  small  eyes  and  in  those  having  a  less  interpupillary  dis- 


Myopia  219 

tance ;  hence,  the  large,  broad  type  of  skull  is  considered  as  a  pre- 
disposing element  in  the  formation  of  myopia. 

Stilling  believes  that  a  low  index  of  the  orbits  is  a  most  im- 
portant predisposing  cause  of  myopia,  since  greater  pressure  is 
exerted  upon  the  eyes  by  the  oblique  muscles  when  the  orbit  is 
low  than  when  there  is  a  greater  interspace  between  the  eyes  and 
the  orbits. 

Insufficient  length  of  the  optic  nerve  has  also  been  assigned 
as  a  possible  cause  of  myopia  (Weiss).  Those  who  have  advo- 
cated this  hypothesis  believe  that  in  certain  cases  the  length  of  the 
optic  nerve  is  not  great  enough  to  permit  free  movement  of  the 
eyeballs,  as  for  the  easy  performance  of  convergence ;  but  this  as- 
sumption is  apparently  irreconcilable  with  the  well-known  fact 
that  a  much  greater  degree  of  adduction  is  always  possible  than 
can  be  manifested  in  convergence. 

The  small  or  negative  angle  alpha,  which,  as  shown  by  Don- 
dcrs,  is  common  in  myopia,  has  also  been  regarded  as  a  factor  in 
the  production  of  this  condition,  since  a  greater  convergence  of 
the  optic  axes  is  required  in  such  eyes  than  when  the  angle  alpha 
is  large. 

In  addition  to  these  theoretical  factors,  there  is  to  be  consid- 
ered the  concurrence — as  supported  by  abundant  clinical  evidence 
— of  visual  defects  in  myopia.  Astigmia,  opacity  of  the  media,  im- 
perfect development  or  atrophy  of  the  retina,  or  other  defect 
which  reduces  the  visual  acuity  may  act  as  a  predisposing  cause  of 
myopia,  since  persons  who  have  such  defects  must  hold  objects 
abnormally  near  the  eyes  in  order  to  increase  the  size  of  the  im- 
ages as  an  offset  to  their  indistinctness. 

On  the  other  hand,  the  relation  between  the  visual  defect  and 
the  myopia  may  not  be  causal ;  both  may  be  manifestations  of  im- 
perfect development  of  the  eye.  This  is,  doubtless,  the  most  po- 
tent predisposing  element  in  the  etiology  of  myopia,  namely,  sub- 
normal resisting  power  of  the  sclera  at  the  posterior  pole  of  the 
eye. 

Posterior  Staphyloma 

So  great  is  the  elongation  in  the  highest  grades  of  myopia 
that  the  sclera  is  reduced  to  paper-like  thinness,  and  owing  to  the 
presence  of  the  underlying  choroid  the  sclera  assumes  a  bluish 
tint.     From  this  fact  the  condition,  first  described  by  Scarpa  in 


220  Errors  of  Refraction 

1807,  received  its  name.*  Scarpa  did  not,  however,  connect  this 
anomaly  with  axial  myopia.  Arlt,  to  whom,  as  we  have  seen,  is 
due  the  credit  of  demonstrating  this  relationship,  erroneously  re- 
garded every  axially  myopic  eye  as  affected  with  staphyloma — a 
term  which  is  correctly  applied  only  when  there  is  demonstrable 
thinning  of  the  sclera  and  atrophy  of  the  choroid  at  the 
posterior  pole  of  the  eye. 

The  Conus. — The  whitish  area,  the  myopic  crescent,  which 
is  often  found  at  the  border  of  the  optic  nerve,  is  called  the  conus. ^ 
The  conus,  which  is  illustrated  in  Fig.  102,  occurs  usually  at  the 
temporal  border  of  the  disk. 

According  to  the  statistics  of  Loring,  this  crescent  is  present 
in  20.5  per  cent  of  myopic  eyes,  in  3.33  per  cent  of  emmetropes, 
and  in  3.49  per  cent  of  hyperopes.  From  these  statistics  the  con- 
clusion is  reached  that  the  conus  bears  an  important  relation  to 


fig.  102  fig.  103 

The  Crescentic  Conus  ■  The    Annular    Conus 

the  origin  of  myopia,  but  that  its  presence  does  not  necessarily  in- 
dicate tendency  to  this  affection. 

The  so-called  annular  or  ring  conus  is  due  to  an  abnormally 
large  opening  in  the  sclera  at  the  entrance  of  the  optic  nerve 
(Fig.  103). 

There  are  .two  opinions  as  to  the  nature  of  the  conus  :  ( 1 ) 
That  it  is  a  circumscribed  atrophy  of  the  choroid,  due  to  stretch- 
ing of  this  membrane  in  axial  elongation,  and  (2)  that  it  is  a  con- 
genital peculiarity  of  development. 

♦From  STeupvA/rj,  a  bunch  of  grapes. 

t  The  conus  (Jaeger)  originally  denoted  the  irregularly  cone-shaped  patch  of 
atrophy  extending  from  the  crescent  in  staphyloma,  but  this  term  is  now  commonly 
used  in  reference  to  the  crescent  or  to  the  exaggerated  scleral  ring. 


Myopia  221 

The  former  hypothesis  is  discredited  by  the  regularity  of  out- 
line of  the  conus,  by  its  occurrence  in  emmetropic  and  hyperopic 
eyes,  and  by  anatomical  examinations,  which  have  shown  that  in 
emmetropia  and  hyperopia  and  also  in  mild  myopia  the  sclera  and 
choroid  are  perfectly  normal  beyond  the  limits  of  the  conus. 

The  second  hypothesis — that  the  conus  is  due  to  congenital 
anomaly  of  development  (absence  of  the  anterior  layers  of  the 
choroid,  pigment,  and  retina) — has  been  strenuously  urged  by 
Schnabel,  who  claims  that  his  opinion  is  confirmed  by  micro- 
scopic examinations. 

Since  it  is  a  matter  of  clinical  observation  that  a  conus  some- 
times appears  in  an  eye  which  has  previously  seemed  free  from 
this  anomaly,  Schnabel  assumes  that  the  conus  was  previously 
present,  but  that,  being  very  small,  it  was  not  noticeable  until, 
with  an  increase  in  the  size  of  the  eye,  there  occurred  a  corre- 
sponding increase  in  the  size  of  the  conus. 

Two  Theories  as  to  the  Origin  of  Posterior  Staphy- 
loma.— In  accordance  with  these  two  theories  as  to  the  na- 
ture of  the  conus,  there  are  two  corresponding  theories  as  to  the 
origin  of  posterior  staphyloma.  Those  who  believe  that  the  conus 
is  ascribable  to  atrophy  of  the  choroid,  believe  also  that  the  strain 
of  near  work  may  give  rise  to  posterior  staphyloma  in  an  eye  of 
perfectly  normal  development.  On  the  other  hand,  those  who  see 
in  the  conus  evidence  of  anomalous  development  believe  that  in 
addition  to  this  defect  there  is  in  all  staphylomatous  eyes  deficient 
development  of  the  sclera  at  the  posterior  polar  region. 

While  the  conus  is  found  in  only  about  20  per  cent  of  myo- 
pic eyes,  it  exists  in  practically  all  in  which  there  is  staphyloma ; 
hence,  if  we  accept  this  theory,  the  presence  of  the  conus  must  be 
regarded  as  evidence,  but  not  positive  evidence,  of  congenital  de- 
ficiency in  resisting  power  of  the  sclera 

Whether  we  do  or  do  not  accept  Schnabel's  views  as  to  the 
nature  of  the  conns,  clinical  evidence  is  largely  in  favor  of  the 
theory  that  staphyloma  occurs  'only  in  eyes  of  congenitally  defec- 
tive development.  None  of  the  influences  which  have  been  detailed 
as  giving  rise  to  myopia  suffices  to  explain  the  occurrence  of 
staphyloma  in  an  eye  of  normal  development.  In  such  an  eye 
the  thickest  and  most  resistant  portion  of  the  sclera  is  in  the  region 
of  the  optic  nerve  and  posterior  pole,  and  any  increase  of  intra- 
ocular pressure  which  might  result  from  near  work  would  not  be 


£r  jction 

limited  in  its  manifestation  to  this  part  of  the  eyeball.  This  b  ex- 
emplified in  glaucoma  in  young  subjects,  in  whom  distention  of  the 
sclera  is  general,  bat  is  most  marked  in  the  region  anterior  to  the 
insertions  of  the  recti  muscles,  where  die  sclera  is  thinner 

The  theory  of  traction  by  the  optic  nerve  is  equally  incapable 
of  accounting  for  the  ectasia  at  the  posterior  pole,  for  the  maxi- 
mum effect  of  such  traction  would  occur  in  the  neighborhood  of 
the  disk,  not  at  the  pole 

In  order  to  explain  by  this  or  other  theory  the  occurrence  of 
the  circumscribed  polar  ectasia,  we  m.  jne  the  coexistence 

either  of  choroidal  inflammation  extending  to  the  sclera  or  of  de- 
development.  Against  the  former  assumption  are  the  clin- 
ical facts  that  choroiditis  does  not  in  general  extend  to  the  sclera. 
and  that  choroidal  complications  occur,  not  before,  but  after  me 
frier."  e::_-  :i 

But  the  most  potent  reason  for  believing  that  the  insufficient 
resisting  power  of  the  sclera  is  congenital  lies  in  the  fact  that  the 
scleral  ectasia  almost  always  commences  at  an  ear*  g  before 
the  ave  been  subjected  to  the  injurious  influences  of  near 

work.  The  eyes  of  newborn  children  are,  as  a  rule,  hyperopic; 
but  it  is  beyond  dispute  that  high  myopia  with  staphyloma  occurs 
at  an  early  age.  Among  other  cases  which  have  been  reported  may 
be  cited  the  following:  myopia  of  u  D  at  the  age  of  eighteen 
months  (Eales),  10  D  at  the  age  of  six  months  (Cant),  17  D  at 
the  age  of  four  yc ars  .    These  are  extreme  cases,  but  the 

occurrence  of  myopia  varying  from  4  D  to  8  D  in  children  under 
ige  is  by  no  means  rare  among  the  poorly-developed 
lower  das.-ef      These  are  the  cases  which,  unless  checked  by  suit- 
able treatment,  always  terminate  in  staphyloma  with  high  myopia. 

Anatomical  and  Ophthalmoscopic  Characteristics. — 
The  thinning  of  the  sclera  in  posterior  staphyloma  is  confined 
mainly  to  the  segment  which  extends  medially  slightly  beyond  the 
edge  of  die  optic  nerve,  and  laterally  to  the  attachment  of  the  in- 
ferior obfique  muscle.  Hie  region  of  the  posterior  pole  or  of  the 
macula  consequently  lies  near  the  center  of  the  staphylomatous 
area,  and  the  greatest  protrusion  occurs  in  this  position.  This  is 
illustrated  in  Fig.  104,  in  which  the  optic  nerve  lies  on  the  side 
of  the  protrusion ;  but  sometimes  the  ectasia  extends  more  medial- 
md  then  die  optic  nerve  lies,  not  as  illustrated,  but  at  the  bot- 
::~   ::  ".-.  z r : * r - 5 : : r. . 


Myopia 

In  connection  with  the  oblique  position  of  the  papilla  there 
occur  also  peculiar  changes  in  the  appearances  of  the  optic  nerve 
in  its  passage  through  the  sclera  and  choroid.  Opposite  to  the 
crescent  the  choroid  and  retina  seem  to  be  drawn  over  the  medial 
border  of  the  nerve,  as  if  the  whole  posterior  portion  of  these 
membranes  had  shifted  its  position.  This  is  the  so-called  super- 
traction  of  the  choroid  of  Xagel  and  Weiss.  Furthermore,  the 
entire  head  of  the  optic  nerve  is  distorted,  as  if  drawn  over  by 


T~.~.      "  "  _ 

.  Lz   r. zz.~.   -~  z    '.'.    i  "  i"    ~  rrj'f:_r   ~  -.\'  -      :    i::     v\- r    i    .i~ z-    '•.::-."'    -'-i:  :      HHfl 

distention  of  the  sclera  towards  the  staphyloma.  This  distortion 
is  accompanfed  also  by  an  abnormal  size  of  the  intervaginal  space, 

-    :  -.:.-  r.rr/t  :.-i  :t-.r.     r:.    :.  21;    :r:~  ::;  r.:rrr.i".  _r.i:hrr.rr.: 
with  consequent  separation  of  the  nerve  sheaths  (Fig.  105 

Ophthalnroscopically  the  oblique  position  of  the  papula  is  a 
marked  characteristic  in  staphyloma.     It  gives  the  disk  an  ap- 

rarer.:.  :vil  :":~;  vh::h  :;  i::fr.:-.::-:t  :  "  r. tr.  ihe  rt: -.1  tr-ir.i; 
over  the  medial  border  of  the  nerve. 

Tiro  Types  of  .-hcic 

In  accordance  with  the  foregoing:  we  condnde  that 

there  are  two  types  of  axial  myopia.  The  first  type  embraces 
those  cases  which  result  mainly  from  the  strain  of  near  work  dur- 
ing school-life,  or  from  other  exacting  eye  work     The  reirac- 

::::    :i.  ir.  :'r\:  :;;■:    h  7  c  r :-?  i ;  :r.  f.-r!y  :hilih::i    i"  :  v,-:-_-";  :~:;:- 
ir.   5:—::  : — 

during  life  if  near  work  were  excluded :  but  the  irritation  induced 
by  the  educational  process  leads  to  an  increase  in  size  of  the  eve. 
zr.i  ::y  :?:i  rer.:!:;  7:::?  rr.:?:  :::fr.  :::.:r_-  :tr  if-  '.'-.-  irei  :•: 
ten  and  twenty  years.    The  progress  of  the  myopia  may  be  arrest- 


224  Errors  of  Refraction 

ed  in  childhood  or  it  may  continue  until  the  body  has  attained  its 
full  growth.  After  this  the  sclera  is  more  resistant,  and  the  myo- 
pia remains  stationary.  It  rarely,  if  ever,  reaches  a  high  degree. 
We  may  assign  6  D  as  the  limit,  beyond  which  it  does  not  often 
pass. 

In  myopia  of  this  type  the  sclera  does  not  undergo  any  appre- 
ciable thinning,  and  neither  ophthalmoscopic  nor  anatomical  exam- 
ination reveals  any  defects  except  the  conus,  which  may  or  may 
not  be  present. 

Although  distant  vision  without  glasses  may  be  very  defect- 
ive, yet  because  this  type  of  myopia  is  not  accompanied  by  atrophic 
and  other  pathological  changes,  all  such  cases  are  classified  as  be- 
longing to  the  mild  type  of  myopia.  Since  such  myopia  is 
acquired  during  school-life,  it  has  also  been  called  acquired  or 
school  myopia. 

The  second  type  of  axial  myopia  embraces  those  cases  which 
are  dependent  upon  posterior  polar  ectasia.  Every  case  of  axial 
myopia  which  exceeds  10  D  may  be  assigned  to  this  class  (Schna- 
bel),  but  even  a  moderate  myopia  (3  D  or  4  D)  occurring  at  an 
early  age  must  be  regarded  as  indicative  of  defective  scleral  de- 
velopment, which  may  subsequently  give  rise  to  staphyloma  with 
great  increase  of  the  myopia. 

The  stretching  of  the  choroid  and  retina  in  staphyloma  is 
first  manifested  by  an  increase  in  size  of  the  crescent,  and  subse- 
quently by  atrophic  changes  in  these  membranes.  The  process 
commences  at  the  outer  border  of  the  crescent ;  the  latter  loses  its 
regular  contour  and  becomes  merged  in  the  larger,  irregularly 
shaped,  whitish  patch.  The  atrophic  area  continues  to  increase 
in  size  and  it  sometimes  surrounds  the  entire  disk,  as  in  Fig.  105 
{annular  staphyloma).  Other  atrophic  patches  appear,  in  the 
worst  cases,  at  or  near  the  macular  region,  and  these  are  very 
disastrous  to  vision.  Moreover,  there  is  interference  with  the 
nutrition  of  the  eye,  so  that  other  grave  dangers  threaten  destruc- 
tion of  the  small  amount  of  vision  which  remains.  Where  the 
atrophic  areas  are  surrounded  by  accumulations  of  pigment,  the 
changes  are  not  recent.  An  ill-defined  yellowish  patch  signifies 
that  the  atrophy  is  still  progressing.  Not  infrequently  the  atrophy 
progresses  by  intermittent  stages,  which  are  distinguished  by 
separating  lines,  more  or  less  defined,  and  marked  at  times  by 
accumulation  of  pigment. 


Myopia 


225 


Since  in  this  class  the  myopia  tends  to  increase,  even  after 
adult  life  is  reached,  and  since  even  when  the  myopia  itself  has 
become  stationary,  atrophy,  hemorrhage,  opacities,  and  retinal 
detachment  still  threaten  the  eye,  the  name  progressive  or  malig- 
nant myopia  is  appropriate. 

Of  those  cases  of  axial  myopia  which  are  more  than  6  D 
and  less  than  10  D,  a  minority  may  be  exaggerated  types  of  ac- 


ne. 105 

Normal  Eye  Posterior   Staphyloma 

A;   Ophthalmoscopic  view.  C:    Ophthalmoscopic  view. 

B;    Diagrammatic   section.  D;  Diagrammatic  section. 

Optic  Nerve   Entrance    ( Hcrmheiser). 

quired  myopia ;  but  for  the  most  part  they  must  be  regarded  as 
favorable  cases  of  staphyloma.  In  fact,  it  is  probable  that  in  all 
such  cases  a  deficiency  in  the  development  of  the  sclera  has  ex- 
isted, and  that  at  least  in  the  greater  proportion  the  elongation 
commenced  prior  to  the  age  of  near  work.  In  those  cases  which 
do  not  become  decidedly  staphylomatous,  the  strength  of  the  sclera 
is  not  greatly  reduced,  so  that  the  elongation  is  arrested  before 
the  development  of  very  high  myopia 


226  Errors  of  Refraction 

Statistics  of  Myopia 

Many  statistics  have  been  published  in  regard  to  myopia. 
In  those  in  which  a  large  number  of  eyes  was  examined,  the  re- 
sults are  fairly  uniform.  These  statistics  relate  mainly  to  the 
proportion  of  myopes  at  different  ages,  in  different  races,  and  in 
different  occupations. 

Of  statistics  which  refer  to  the  proportion  of  myopes  at  dif- 
ferent ages  and  in  different  races,  Loring  attaches  especial  im- 
portance to  the  results  of  four  observers :  Brismann,  of  St.  Pe- 
tersburg; Conrad,  of  Konigsberg,  and  Derby  and  Loring,  of  New 
York.  A  large  number  of  eyes  was  examined  by  each  of  these 
observers,  and  the  conditions  were  similar  in  all  cases.  The  ex- 
aminations were  all  made  on  school-pupils  between  the  ages  of  six 
and  twenty-one  years. 

According  to  Erismann's  statistics  (4358  pupils),  10  per 
cent  were  myopic  in  the  lowest  classes,  the  proportion  increasing 
to  42  per  cent  in  the  highest;  Conrad's  statistics  (3036  pupils) 
showed  11  per  cent  of  myopia  in  the  lowest  classes  and  62  per 
cent  in  the  highest;  Derby  and  Loring' s  {226$  pupils)  showed  3.5 
per  cent  in  the  lowest  and  about  27  per  cent  in  the  highest  classes. 

Many  other  investigators  have  published  statistics  bearing  on 
this  subject,  but  those  here  given  are  sufficient  to  convince  us 
that  myopia  is  very  frequently  acquired  during  school-life,  and 
that  Americans  are  much  less  subject  to  this  affection  than  Euro- 
peans. 

Statistics  have  also  been  published  showing  the  change  in  re- 
fraction in  the  same  individuals  with  increase  of  age.  Among 
these  may  be  mentioned  those  of  Brismann  (350  eyes  re-exam- 
ined after  the  lapse  of  six  years),  of  Reich  (85  pupils,  after  six 
years),  and  of  Cohn  (138  pupils,  after  one  and  one-half  years). 
These  statistics  all  show  that  there  is  a  general  tendency  to  in- 
crease of  refraction  (diminution  of  hyperopia  or  increase  of 
myopia)  prior  to  adult  life,  and  that  this  tendency  is  most  marked 
in  those  who  are  already  myopic.  In  no  case  do  they  show  that 
an  eye  previously  recorded  as  hyperopic  or  emmetropic  has  at- 
tained a  degree  of  myopia  exceeding  6  D. 

Of  the  statistics  relating  to  the  degree  of  myopia  among  a 
large  number  of  myopes,  those  of  Schweizer  must  be  mentioned 
as  being  particularly  useful.     Among  5039  myopic  eyes  the  myo- 


Myopia  227 

pia  did  not  exceed  6  D  in  4029  of  these;  in  475  eyes  it  was  be- 
tween 7  D  and  10  D,  and  in  535  eyes  it  was  more  than  10  D. 

T scheming  has  published  very  instructive  data  showing  the 
proportion  and  grade  of  myopia  among  different  classes  of  per- 
sons. He  found  that  of  2336  eye-workers,  18  per  cent  were  myo- 
pic; of  5187  laborers,  4  per  cent  were  myopic.  But  of  the  myopic 
eye-workers,  only  3  per  cent  had  myopia  exceeding  9  D,  while  of 
the  myopic  laborers  18  per  cent  had  myopia  exceeding  9  D.  These 
figures  indicate  very  clearly  that  while  near  work  has  a  decided 
influence  in  the  etiology  of  mild  and  moderate  degrees  of  myopia, 
it  is  not  a  predominant  factor  in  the  production  of  posterior  sta- 
phyloma. 

Statistics  have  also  been  published  with  a  view  to  showing, 
by  comparison  with  the  older  statistics,  the  beneficial  effect  which 
hygienic  care  of  the  eyes  of  the  young  has  exerted  upon  the  pro- 
portion of  myopes.  Risley  especially  has  made  extensive  investi- 
gations of  this  subject.  His  data,  as  well  as  those  of  others,  in- 
dicate that  a  perceptible  improvement  follows  the  introduction 
of  school  hygiene. 

Lastly,  statistics  have  been  published  setting  forth  the  influ- 
ence of  heredity  in  the  etiology  of  myopia.  These  statistics  show 
not  only  that  some  races  are  more  liable  than  others  to  myopia, 
but  also  that  the  members  of  certain  families  possess  in  a  special 
degree  the  characteristics  which  lead  to  the  formation  of  this 
anomaly. 

Symptoms  of  Myopia 

Myopia  of  every  grade  is  characterized  by  one  predominant 
symptom: — the  inability  to  see  distant  objects  clearly.  Even  in 
myopia  of  .5  D  vision  at  six  meters  or  more  is  perceptibly  below 
the  normal.  But  as  the  power  of  analyzing  objects  varies,  so 
with  the  same  amount  of  error  the  vision  will  vary  according  to 
the  intelligence  of  the  individual,  the  familiarity  with  the  object 
under  examination,  and  the  size  of  the  pupil  of  the  eye. 

The  symptoms  of  eye-strain  (asthenopia  and  congestion  of 
the  retina)  which  were  described  as  occurring  in  hyperopia  occur 
also  in  myopia.  These  symptoms  are  regarded  by  some  ophthal- 
mologists as  indicating  that  the  ocular  membranes  are  undergoing 
a  process  of  stretching.  Whether  or  not  this  is  the  case,  such 
symptoms  can  not  be  said  to  play  an  important  part  in  the  etiology 


228  Errors  of  Refraction 

of  staphyloma,  since  they  frequently  occur  in  eyes  in  which  the 
elongation  never  passes  the  limit  of  emmetropia. 

Muscular  asthenopia,  due  to  disturbance  in  the  relation  be- 
tween accommodation  and  convergence,  is  a  not  uncommon  symp- 
tom in  myopia.  Owing  to  the  weak  accommodative  impulse  re- 
quired, the  convergence-center  is  insufficiently  stimulated,  and 
insufficiency  of  convergence  results. 

Insufficiency  of  convergence  occurring  in  myopia  may  be  due 
not  only  to  the  disturbed  relation  between  accommodation  and 
convergence,  but  also  to  some  anatomical  peculiarity  requiring 
unusual  effort  to  produce  convergence,  such  as  abnormally  great 
interpupillary  distance,  elongated  eyeball,  or  unfavorable  inser- 
tions of  the  internal  recti  muscles. 

Divergent  Strabismus  in  Myopia. — When  the  myopia 
exceeds  4  D,  so  that  the  far-point  is  less  than  one-fourth  of  a 
meter  from  the  eye,  binocular  near  work  is  almost  always 
burdensome,  because  of  the  great  tax  on  the  convergence.  On 
this  account  myopes  of  this  class  generally  abandon  binocular  vis- 
ion (if  they  do  not  wear  correcting  lenses),  using  only  one  eye  in 
near  work,  while  the  other  eye  turns  relatively  outward  to  a 
greater  or  less  degree.  The  parallel  direction  may  be  maintained 
in  distant  vision ;  but  frequently  binocular  distant  vision  is  aban- 
doned, and  the  unused  eye  becomes  permanently  divergent,  the 
latent  insufficiency  passing  into  manifest  strabismus.  Hence,  di- 
vergent strabismus  is  a  not  infrequent  symptom  of  myopia,  and 
especially  of  that  exceeding  4  D. 

Symptoms  Arising  from  Disturbed  Nutrition  in 
Staphyloma. — In  the  high  grades  of  myopia  the  far-point  lies 
only  a  few  centimeters  from  the  eye,  and  consequently,  reading 
matter  or  small  objects  to  be  deciphered  must  be  held  just  beyond 
the  tip  of  the  nose;  but  this  is  by  no  means  the  gravest  symptom 
of  staphyloma.  Those  symptoms  which  arise  from  defective 
nutrition  of  the  eye  are  such  as  to  give  to  the  myopia  a  position 
of  secondary  importance.  Floating  opacities  in  the  vitreous  body, 
high  astigmia  from  partial  dislocation  of  the  lens,  polyopia 
from  commencing  cataractous  degeneration,  fixed  scotomata  from 
retinal  atrophy  or  hemorrhage,  metamorphopsia  from  serous  ef- 
fusion beneath  the  retina,  and  total  blindness  from  retinal  detach- 
ment are  among  the  complications  that  are  liable  to  occur  in 
myopia  with  posterior  staphyloma. 


Myopia  229 

Diagnosis  of  Myopia 

Externally  there  is  nothing  markedly  characteristic  of  mild 
myopia ;  but  the  elongation  in  staphylomatous  eyes  is  apparent  in 
the  facial  expression.  Such  eyes  are  usually  prominent  and  their 
large  size  is  especially  noticeable  when  they  are  turned  sharply  to 
one  side.  In  addition,  there  is  generally  found  an  abnormal 
depth  of  the  anterior  chamber  in  the  highest  grades  of  myopia. 
These  appearances  are,  however,  mere  incidentals,  since  the  my- 
opia and  its  degree  may  be  readily  determined  by  application  of 
the  tests  which  were  enunciated  in  Chapter  X. 

The  order  of  applying  these  tests  which*  was  suggested  for 
the  measurement  of  hyperopia  may  be  followed  also  in  myopia, 
namely,  ophthalmometry  (for  the  determination  of  coexisting  as- 
tigmia),  skiascopy,  ophthalmoscopy,  and  the  subjective  ex- 
amination with  trial  lenses. 

The  rule  which  was  advised  for  the  employment  of  a  cyclo- 
plcgic  in  hyperopia  is  applicable  also  in  myopia.  While  perhaps 
in  a  greater  proportion  of  cases  the  true  refractive  condition  may 
be  ascertained  without  cycloplegia  in  myopia  than  in  hyperopia, 
yet  there  is  no  certainty  as  to  the  correctness  of  the  result  in 
young  persons  unless  the  accommodation  has  been  paralyzed. 

The  ophthalmoscopic  examination  assumes  a  relatively  great- 
er importance  in  myopia  than  in  hyperopia,  since  by  it  we  are  in- 
formed as  to  the  condition  of  the  interior  of  the  eye — whether 
the  myopic  crescent,  choroidal  atrophy,  macular  disease,  opacity 
of  the  vitreous  body,  or  other  accompaniment  of  staphyloma  is 
present. 

Differentiation  of  Mild  and  Malignant  Myopia. — 
There  are  three  points  to  be  especially  considered  in  making 
the  distinction  between  these  two  kinds  of  axial  myopia: 

(1.)  The  Age  at  which  the  Myopia  Develops. — Myopia  oc- 
curring before  the  age  of  near  work  always  indicates  defective 
scleral  development,  which,  unless  promptly  arrested,  will  prob- 
ably terminate  in  staphyloma.  On  the  other  hand,  myopia  which 
is  evolved  from  a  condition  of  hyperopia  during  school-life,  is 
indicative  of  the  mild  form  and  will  not  lead  to  destructive  pro- 
cesses in  the  eye. 

(2.)  The  Degree  of  Myopia. — Myopia  which  is  less  than  6  D 
in   an   adult  may  be   regarded   as  having  been  acquired  during 


230  Errors  of  Refraction 

school-life  and,  therefore,  as  belonging  to  the  mild  form ;  or,  ex- 
ceptionally, it  may  denote  an  infantile  myopia  in  which  the  prog- 
ress of  ectasia  has  been  arrested,  and  in  which  further  advance 
is  not  to  be  expected.  Myopia  which  is  between  6  D  and  10  D 
must  be  regarded  as  probably  due,  in  adults,  to  arrested  ectasia; 
in  youth  an  advancing  process  must  be  assumed.  Myopia  exceed- 
ing 10  D  always  indicates  staphyloma. 

(3.)  The  Ophthalmoscopic  Appearances. — The  presence  of 
the  conus  is  evidence  of  staphyloma  only  in  that  while  frequently 
absent  in  mild  myopia  it  is  always  found  in  staphyloma.  Positive 
proof  of  staphyloma  is  afforded  by  the  existence  of  choroidal  atro- 
phy extending  beyond  the  border  of  the  crescent  with  or  without 
atrophy  in  the  macular  region. 

Diagnosis  of  Curvature-Myopia  and  Index-Myopia. — 

In  the  small  minority  of  cases  in  which  high  myopia  is  due 
to  conical  cornea,  the  characteristics  are  altogether  different  from 
those  in  axial  myopia.  The  symptoms  of  posterior  staphyloma 
are  absent,  while  the  excessive  curvature  of  the  central  portion  of 
the  cornea  is  revealed  by  keratometry,  by  skiascopy,  and  by  the 
unaided  eye  in  advanced  cases. 

The  myopia  which  occurs  in  old  age  from  swelling  or  increase 
of  density  of  the  nucleus  of  the  lens  is  also  readily  differentiated 
from  axial  myopia  by  the  period  of  life  at  which  it  develops,  by 
the  abnormally  intense  nuclear  reflex,  and  by  the  detection  of  len- 
ticular opacities. 

Treatment  of  Myopia 

Since  it  is  well  established  that  prolonged  near  work  tends 
to  favor  the  myopic  state  of  refraction,  and  since  it  would  be  a 
grave  misfortune  if,  with  the  advance  of  civilization,  myopia 
should  become  the  ordinary  condition  of  the  human  eye,  we  must 
do  all  that  is  in  our  power  to  combat  this  tendency  by  hygienic 
and  artificial  means.  Whatever  acts  favorably  in  the  individual 
exerts  also  a  beneficial  influence  upon  the  resisting  power  of  the 
eyes  of  future  generations. 

Prophylactic  Measures. — Young  children  should  not  be 
permitted  to  indulge  in  exacting  near  work,  since  it  is  at  this 
period  that  the  sclera  is  most  distensible.  They  should  not  com- 
mence school  before  the  completion  of  the  seventh  year  of  age; 
and  at  the  beginning  of  school-life  and  at  least  once  a  year  there- 


Myopia  231 

after  the  vision  should  be  tested  in  order  that  those  in  whom  it  is 
found  defective  may  receive  appropriate  treatment. 

The  correction  of  astigmia  is  especially  important,  since 
the  defect  of  vision  caused  by  it  necessitates  an  abnormal  approx- 
imation of  objects,  with  excessive  strain  on  the  accommodation 
and  convergence. 

When  the  vision  is  markedly  defective  and  is  incapable  of 
improvement,  the  child  should  not  be  permitted  to  pursue  the 
full  course  of  study  required  of  healthy  children. 

Since  anything  that  interferes  with  the  bodily  nutrition  must 
exert  an  unfavorable  influence  upon  the  strength  of  the  sclera, 
and  since  posterior  staphyloma  is  most  liable  to  occur  in  children 
of  defective  constitution,  it  is  essential  that  school  hours  should 
be  broken  by  suitable  out-of-door  exercise,  and  that  other  mat- 
ters of  general  hygiene  should  receive  proper  attention. 

Of  no  less  importance  are  the  arrangements  of  the  school- 
rooms as  to  light  and  ventilation,  and  the  adaptation  of  the  desk 
to  the  pupil  (for  the  avoidance  of  the  stooping  posture  with  the 
consequent  congestion  of  the  head  and  eyes),  and  the  quality 
of  the  paper  and  print  used  in  the  text-books.  Much  thought  has 
been  given  this  subject  of  school  hygiene  of  late  years,  and  great 
improvements  have  been  effected. 

The  attention  given  these  matters  should  extend  also  to  office 
rooms  and  factories,  in  which  the  eyes  of  the  employees  are  taxed 
to  the  utmost  during  a  period  of  eight  or  ten  hours  each  day.  In 
those  occupations  which  necessitate  the  prolonged  examination 
of  small  objects,  a  magnifying  glass,  such  as  is  used  by  watch- 
makers, should  be  employed  as  far  as  possible.  By  this  means 
both  accommodation  and  convergence  are  relieved  of  the  strain 
to  which  they  would  otherwise  be  exposed. 

Use  of  Lenses  in  Myopia. — While  all  authorities  are 
agreed  as  to  the  beneficial  effect  of  hygienic  measures,  the  influ- 
ence of  correcting  lenses  upon  existing  myopia  is  a  question  about 
which  there  has  been  some  difference  of  opinion.  Those  who  be- 
lieve the  myopia  to  be  the  result  of  over-exercise  of  accommoda- 
tion condemn  the  use  of  concave  lenses  in  near  work.  Those, 
on  the  other  hand  (including  the  large  majority  of  ophthalmolo- 
gists of  the  present  day),  who  believe  that  convergence,  not  ac- 
commodation, is  the  main  factor  in  the  production  of  myopia, 
deny  any  evil  effect  of  concave  lenses.    Furthermore,  it  is  claimed 


232  Errors  of  Refraction 

that  by  restoring  the  eye  to  its  normal  condition  of  emmetropia, 
a  beneficial  influence  is  exerted  upon  the  progress  of  the  myopia. 
In  support  of  this  view  is  the  clinical  fact  that  with  the  relief 
from  asthenopia  effected  by  the  constant  use  of  glasses,  the  prog- 
ress of  the  myopia  is  frequently  checked. 

As  in  hyperopia,  so  in  myopia,  no  general  rule  can  be  given 
for  the  prescription  of  lenses;  but  there  is  this  difference:  in 
hyperopia  correction  is  not  essential  as  long  as  the  condition  gives 
rise  to  no  disturbance,  and  the  younger  the  child  the  less  com- 
monly is  correction  required  (except  in  strabismus)  ;  whereas 
myopia  occurring  in  childhood  requires  correction  in  every  in- 
stance and  at  the  earliest  age  compatible  with  the  wearing  of 
spectacles. 

In  childhood  and  youth  the  entire  myopia,  or  all  but  a  small 
fraction,  should  be  corrected  and  the  glasses  should  be  ordered 
for  constant  wear.  But  in  myopes  who  have  passed  early  adult 
life  without  correction  of  their  refractive  error,  the  ciliary  muscle 
is  untrained  and  imperfectly  developed,  and  total  correction  of  the 
myopia  will  not  be  tolerated  for  near  work.  The  course  to 
be  pursued  in  these  cases  varies  with  the  degree  of  myopia  and 
with  the  attendant  circumstances.  We  may  make  the  following 
classification : 

(1)  When  the  myopia  is  not  more  than  3.5  D  or  4  D,  and 
especially  if  the  presbyopic  age  has  been  reached,  lenses  may  be 
used  for  distance,  while  near  work  is  performed  without  the 
myopic  correction. 

(2)  When  the  myopia  exceeds  4  D,  vision  being  binocular, 
concave  lenses  are  imperative  in  near  work,  since  without  lenses 
the  strain  on  the  convergence  is  too  great  to  be  comfortably  and 
safely  endured.  The  far-point  must  be  so  removed  by  lenses 
that  no  more  than  3.5  ma  or  4  ma  of  convergence  will  be  re- 
quired. 

(3)  When  vision  is  monocular  concave  lenses  are  not  usually 
acceptable  in  near  work,  since  larger  images  are  obtained  without 
the  lenses,  and  without  any  exercise  of  accommodation  or  of  con- 
vergence. In  this  class,  to  which  belong  the  majority  of  those 
having  myopia  of  high  degree  (which  has  not  been  corrected  in 
early  life),  concave  lenses  are  in  many  cases  rejected  also  for 
distant  vision,  or  are  accepted  only  for  momentary  use: 

The  treatment  of  muscular  disturbances  directly  dependent 


Myopia  233 

upon  myopia  consists  in  the  application  of  the  appropriate  con- 
cave lenses,  and  the  earlier  the  age  at  which  relief  is  sought,  the 
greater  is  the  likelihood  of  a  successful  result.  Other  measures, 
which  may  be  required  in  neglected  cases,  are  described  in  Chap- 
ter XVII. 

Use  of  Tinted  Glasses. — Although  tinted  glasses  are  not 
advisable  for  permanent  wear  in  healthy  conditions  of  the  eye 
tunics,  such  glasses  are  sometimes  required  in  the  diseased  con- 
ditions attending  high  myopia. 

Secondary  Effects  of  Concave  Lenses. — The  secondary 
effects  of  concave  lenses  are  opposite  to  those  which  were  noted 
(Chapter  XI)  as  occurring  in  the  use  of  convex  lenses.  There 
are  chiefly  to  be  considered  the  prismatic  effect,  the  actual 
minification  of  the  retinal  image,  and  the  apparent  minification 
due  to  the  erroneous  judgment  as  to  the  distance  of  the  object. 
There  is  also  alteration  in  the  relation  between  accommodation 
and  convergence,  which  may  give  rise  to  disturbance  when  the 
lenses  are  first  worn;  but  more  frequently  this  change  is  advan- 
tageous, since  insufficiency  of  convergence  is  very  common  in 
uncorrected  myopia. 

Prescription  of  Concave  Lenses. — The  directions  which  were 
given  for  the  prescription  of  convex  lenses  apply  also  to  the 
ordering  of  concave  lenses. 

Concave  lenses  are  usually  supplied  either  in  the  biconcave 
or  the  periscopic  form.  In  the  latter  the  outer  face  of  the  lens 
has  the  curvature  of  a  plano-convex  lens  of  -\-  1.25  D,  while  the 
appropriate  concavity  is  ground  on  the  other  surface,  which  is 
placed  towards  the  eye.  In  the  absence  of  any  special  instruc- 
tions, the  optician  would  be  at  liberty  to  use  his  discretion  in  the 
choice  between  these  two  forms.  If  a  greater  periscopic  effect  is 
desired  than  that  which  is  afforded  by  the  ordinary  form  of  the 
periscopic  lens,  the  required  degree  of  concavity  must  be  speci- 
fied. 

Operative  Treatment  of  Axial  Myopia. — Because 
of  the  disadvantages  attending  the  use  of  strong  concave  lenses, 
with  the  consequent  rejection  of  them  by  many  myopes,  it  was 
many  years  ago  proposed  that  the  crystalline  lens  should  be  re- 
moved for  the  relief  of  such  persons.  It  is  said  that  this  pro- 
cedure  was   first   suggested   by   Gottlieb   Richter,   of   Gottengen, 


234  Errors  of  Refraction 

about  the  year  1790.  It  was  not  carried  into  execution,  however, 
until  Moor  en,  in  1854,  performed  a  discission  operation  upon  an 
eye  affected  with  high  myopia.  This  case  was  successful,  but  later 
Mooren  met  with  failure,  and  the  method  fell  into  ill  repute,  until 
in  1887  Fukala  revived  it  by  operating  successfully  in  a  number  of 
cases.  Other  ophthalmologists  followed  Fukala's  example  and 
many  hundreds  of  cases  have  been  reported.  The  operation  as 
now  usually  performed  consists  of  two  stages.  In  the  first  stage 
the  lens  is  rendered  cataractous  by  discission,  while  the  second 
stage  consists  in  removal  of  the  lens  through  a  linear  incision.  An 
interval  of  a  few  days  must  elapse  between  the  two  stages,  the 
exact  time  being  determined  by  the  condition  of  the  lens  and  the 
tension  of  the  eye. 

While  removal  of  the  lens  is  a  much  safer  procedure  at  the 
present  day  than  it  was  when  Mooren  first  undertook  it  for  the 
cure  of  myopia,  yet,  owing  to  the  diseased  condition  of  the  eye  in 
posterior  staphyloma,  the  operation  must  always  be  attended  with 
serious  risks,  as  of  hemorrhage  and  detachment  of  the  retina. 
This  method  is,  therefore,  limited  in  application.  It  is  especially- 
indicated  in  those  persons  in  whom  continuance  in  their  occupa- 
tion is  impossible  without  some  greater  improvement  of  vision 
than  can  be  obtained  from  glasses.  The  operation  is  contraindi- 
cated  in  old  persons.  As  a  rule,  forty  years  should  be  regarded 
as  the  age  limit  {Fukala),  though  older  persons  have  been  oper- 
ated on  successfully. 

The  effect  of  removal  of  the  lens  upon  the  refractive  con- 
dition of  the  eye  and  upon  the  size  of  retinal  images  varies  with- 
the  axial  length  (Chapter  V).  We  have  learned  that  if  the  re- 
fracting surfaces  are  normal  in  position  and  curvature,  about 
24  D  of  myopia  will  be  neutralized  by  removal  of  the  lens,  and 
that  the  linear  dimensions  of  the  retinal  image  will  be  about  one 
and  one-half  times  as  large  as  in  the  normal  eye.  In  practice 
these  figures  are  only  approximately  correct.  As  the  degree  of 
alteration  in  the  refractive  condition  produced  by  lens-removal 
diminishes  with  the  axial  length,  the  degree  of  myopia  which  may 
furnish  emmetropia  in  the  aphakic  condition  varies  within  quite 
wide  limits.  A  condition  approximating  emmetropia  may  result 
from  removal  of  the  lens  in  myopia  varying  from  16  D  to  25  D. 
Because  of  the  great  individual  variation,  the  empiric  rules  which 
have  been  given,  as  the  result  of  averages  deduced  from  numerous 


Myopia  235 

operations,  are  of  no  practical  assistance  in  determining  the 
probable  post-operative  refractive  condition. 

In  view  of  the  foregoing  considerations,  it  is  apparent  that 
operative  procedure  is  contraindicated  when  vision  is  so  low  from 
macular  degeneration  that  the  improvement  to  be  expected  from 
enlargement  of  images  (and  in  some  cases  from  the  removal  of 
an  imperfectly  transparent  and  irregularly  refracting  lens)  could 
afford  no  useful  sight.  The  least  degree  of  myopia  in  which  re- 
moval of  the  lens  is  permissible  is  about  1.2  D,  and  usually  15  D 
is  a  more  appropriate  limit. 

Operative  Treatment  of  Conical  Cornea. — Since 
only  a  small  proportion  of  the  extremely  high  myopia  caused  by 
conical  cornea  would  be  relieved  by  removal  of  the  lens,  such 
treatment  would  be  of  no  material  benefit  in  this  affection.  In 
order  to  ameliorate  the  distressing  condition  of  the  subjects  of 
this  disease  (lenses  being  particularly  unsatisfactory  because  of 
the  hyperboloidal  form  of  the  cornea),  cauterization  of  the  apex 
of  the  corneal  protrusion  has  been  advocated  and  practised  by 
ophthalmic  surgeons.  The  excessive  curvature  is  diminished  by 
the  flattening  which  takes  place  with  the  process  of  healing.  A 
subsequent  iridectomy  may  be  required  on  account  of  the  central 
scar-formation. 

The  following  authorities  have  been  consulted  in  the  prep- 
aration of  the  foregoing  chapter : 

Aristotle,  Opera  (Didot's  Greek-Latin  Ed.),  Prob.,  Sec. 
XXXI. 

Donders,  Anomalies  of  Refraction  and  Accommodation. 

Landolt,  Refraction  and  Accommodation  of  the  Bye. 

De  Schweinitz,  Myopia  in  Diabetes,  Ophthal.  Record,  1897. 

Scarpa,  A  Treatise  on  the  Principal  Diseases  of  the  Eye, 
Eng.  ed.  by  Briggs. 

Beer,  Lehre  der  Augenkrankheiten. 

Schnabel,  Relationship  of  Staphyloma  Posticum  to  Myopia, 
Norris   and   Oliver's   System    of  Diseases  of  the   Eye. 

Arlt,  Die  Krankheiten  des  Auges,  Bd.  Hi.;  and  Ucber  die 
Ursachen  und  die  Bntstehung  der  Kurzsichtheit. 

Hensen  und  Voelckers,  Ueber  die  Ac commodationsbewegung 
der  Choroidea  in  Auge  des  Menschen,  Arch,  fur  Ophthal.,  1873. 


236  Errors  of  Refraction 

Hess  und  Heine,  Arbeiten  aus  dem  Gebiete  der  Accom., 
Arch,  fur  Ophthal.,  1898. ' 

Stilling",  Untersuchungen  Ueber  die  Enstehung  der  Kurssich- 
tigheit. 

Fuchs,  Text  Book  of  Ophthalmology. 

Heine,  Contribution  to  the  Anatomy  of  the  Myopic  Bye, 
Arch,  of  Ophthal.,  1902. 

Jaeger,  Ueber  die  Einstellungcn  des  Dioptrischen  Apparates 
in  Mensch.  Auge. 

Weiss,  Beitrdge  Zur  Anat.  des  Myop.  Auges,  Mittheilungen 
aus  der  Ophthal.  Klinik  in  Tubingen,  Hft.  iii. 

Schnabel  und  Herrnheiser,  Ueber  Staphyloma  Posticum, 
Conns,  und  Myopic,  Zeitschrift  fur  Heilkunde,  1895. 

Herrnheiser,  Das  kurzsichtige  Auge,  Augenartztliche  Unter- 
sichtstafeln  (Magnus). 

Loring.  Are  Progressive  Myopia  and  Conus  due  to  Heredi- 
tary Predisposition,  etc.?  Int.  Med.  Cong.,  Phila.,  1876. 

Motais,  De  I'Heredite  de  la  Myopic,  Arch.  d'Opth.,  1889. 

Priestley  Smith,  Wray,  Eales  and  Cant,  Discussion  of  the 
Causes  and  Prevention  of  Myopia,  British  Med.  Journal,  1890, 
Vol.  II. 

Risley,  Genesis  and  Treatment  of  the  Myopic  Eye,  Jour.  A. 
M.  A.,  1902 ;  and  School  Hygiene,  Norris  and  Oliver's  System 
of  Diseases  of  the  Eye. 

Erisman,  Bin  Beitrag  zur  Entzvickelungs  Gesichte  der  Myo- 
pic gestulzt  auf  die  Untersuchung  4358  Schulem  und  Schulern- 
nen,  -Arch,  fiir  Ophthal.,  1871 ;  and  Die  Hygiene  der  Schule,  Pett. 
u.  Ziemms,  Handbuch  der  Hygiene,  Vol.  II. 

Tscherning,  Studicn  Ueber  die  Aetiologic  der  Myopic,  Arch, 
fiir  Ophthal,  1883. 

Cohn,  Hygiene  of  the  Eyes. 

Reich,  Refractionsverandcrungen  im  Laufc  von  sechs 
Jahren  an  85  Schulem  beobachtet,  Arch,  fiir  Ophthal.,  1883. 

Schweizer,  Ueber  die  deletdren  Folgen  der  Myopic,  etc.,  Arch, 
fiir  Augenheilkunde,  1880. 

Fukala,  Heilung  hochstgradiger  Kurzsichtigheit. 

Mooren,  Die  medicinische  und  Operative  Behandlung  Kurz- 
sichtiger  Storungen. 

Knapp,  Operations,  etc.,  Norris  and  Oliver's  Systems  of  Dis- 
eases of  the  Bye,  and  Five  Cases  of  Keratoconus  Treated  with 
the  Galvano- Cautery,  Arch,  of  Ophthal.,  1892. 


CHAPTER  XIII 


ASTIGMIA 


Astigmia  of  the  eye  (As),  usually  called  astigmatism,  has 
already  been  defined  as  that  condition  in  which,  because  of  irregu- 
larity or  asymmetry  of  refraction,  homocentric  rays  lose  their 
homocentric  character  in  passing  through  the  ocular  media. 

We  have  learned  that  there  are  two  kinds  of  astigmia, 
regular  and  irregular,  according  as  the  defect  is  due  to  asymmetry 
or  irregularity  of  refraction.  As  the  word  astigmia  (or  astig- 
matism) is  used  without  qualification  it  refers  to  the  regular 
variety  of  this  anomaly. 

Astigmia  was  noted  by  Thomas  Young  (1801),  who  by 
means  of  his  optometer  discovered  that  he  had  this  defect  in 
his  own  eye. 

Young  excluded  asymmetry  of  the  cornea  in  his  case  by 
immersing  the  eye  in  water  (by  which  means  the  corneal  refrac- 
tion is  almost  entirely  neutralized),  replacing  the  corneal  refrac- 
tion by  the  action  of  a  convex  spherical  lens,  and  observing  that 
the  astigmia  remained  unchanged.  Since  the  defect  was  not  in 
the  cornea,  he  inferred  that  it  was  due  to  an  oblique  position  of  the 
crystalline  lens. 

Sir  George  Airy,  who  had  myopia  with  astigmia,  first 
wore  spectacles  correcting  the  defect  (1827),  but  the  introduc- 
tion of  cylindrical  lenses  into  common  use  was  accomplished 
through  the  advocacy  of  Bonders.  Our  practical  knowledge 
of  astigmia  dates  from  the  invention  of  the  ophthalmometer 
by  Helmholtz,  and  from  its  use  by  him,  by  Donders,  Knapp,  and 
others. 

No  definite  name  was  given  either  by  Young  or  by  Airy  to  the  anomaly 
which  they  discovered  in  their  own  eyes.  Later  Dr.  Whew  ell,  an  eminent 
scholar  and  a  friend  of  Airy,  suggested  that  this  defect  be  called  astig- 
matism. This  word  soon  came  into  general  use,  and  even  at  the  present 
time  it  is  the  commonly  accepted  term. 

Attention  was  first  called  to  the  incorrectness  of  the  word  astigmatism 
by  Dixon,  who,  in  an  article  on  Vision  in  Holmes'  System  of  Surgerv 
(1881)  wrote: 

"Astigmism  would  be  the  more  correct  term  trny^  { trriyy.^)  being 
commonly   used   by    Greek   writers   to   express   a   geometric   point,    while 

•  237 


238  Errors  of  Refraction 

ori-y^a  (o-Ti-yjioTos)  always  signifies  something  material,  more  or  less 
visible  or  tangible — a  puncture,  mark  or  spot.  I  took  the  liberty  of  point- 
ing this  out  to  the  late  eminent  scholar,  Dr.  Whewell,  who  had  originally 
suggested  the  word  astigmatism,  and  he  approved  of  astigmism  as  being 
etymologically  the  better   formed  word." 

The  word  astigmism,  which  Dixon  suggested,  is  not  much  more  de- 
sirable than  the  word  which  it  was  intended  to  replace.  It  would  be 
manifestly  unwise  to  attempt  to  reform  our  terminology  solely  for  ety- 
mological reasons,  as  this  would  involve  us  in  many  difficulties. 

Astigmia,  the  word  which  I  have  adopted,  has  a  more  agreeable  sound, 
and  it  also  has  the  advantage  that  it  has  to  some  extent  come  into  use. 

None  of  the  foregoing  words  makes  the  distinction  between  asym- 
metrical refraction  in  general  and  such  refraction  as  a  defect  of  the  eye. 
The  latter  condition  would  be  properly  called  astigmopia,  but  this,  being  a 
somewhat  cumbersome  and  an  unfamiliar  word,  would  probably  not  find 
ready  acceptance.  I  have,  however,  made  use  of  the  word  astigmope,  as 
corresponding  with  myope  and  hyperope,  since  there  is  no  other  word 
which  conveniently  takes  its  place. 

The  physiological  astigmia  which  results  from  slight 
imperfection  is  not  noticeable  in  ordinary  vision,  but  when  one 
looks  at  a  point  of  light,  as  a  star,  the  image  on  the  retina  is  not 
a  point,  as  it  would  be  if  the  eye  were  perfectly  formed.  Owing 
to  irregular  astigmia,  the  star  appears  as  a  bright  center  with 
lines  of  light  (rays)  proceeding  in  various  directions  from  this 
center.  The  more  free  an  eye  is  from  astigmia  the  less 
marked  is  the  ray-like  appearance.  But  that  such  appearance  is 
well-nigh  universal  is  attested  by  the  time-honored  custom  of 
picturing  a  star,  not  as  a  round  body,  but  as  sending  forth 
streams  of  light  in  various  directions. 

Etiology  of  Corneal  Astigmia 

Regular  corneal  astigmia  is  due,  in  the  vast  majority  of 
cases,  to  asymmetrical  development  of  the  eyeball — a  defect  which 
is  usually  congenital,  though  it  is  sometimes  acquired  after  birth. 

We  have  learned  that  in  those  eyes  which  may  be  regarded 
as  normal  the  curvature  of  the  cornea  is,  as  a  rule,  slightly 
greater  in  the  vertical  than  in  the  horizontal  meridian.  In 
assuming  this  form  the  cornea  follows  the  form  of  the  eyeball, 
which  is  slightly  shorter  in  the  vertical  than  in  the  horizontal 
diameter;  and  this,  in  turn,  conforms  to  the  shape  of  the  orbit, 
which  offers  its  least  dimension  in  the  vertical  meridian.  Exag- 
geration of  this  normal  asymmetry  gives  rise  to  astigmia  in 
excess  of  the  amount  which  can  be  regarded  as  physiological. 

Relation  of  Astigmia  to  Cranial  Development. — 
But  the  foregoing  explanation  serves  only  for  such  asymmetry 


Astigmia  239 

as  presents  the  greatest  curvature  in  the  vertical  meridian.  Occa- 
sionally the  cornea  presents  its  least  curvature  in  the  vertical 
meridian,  the  greatest  curvature  being  in  the  horizontal  meridian, 
or  the  meridians  of  greatest  and  least  curvature  may  be  neither 
vertical  nor  horizontal  (oblique).  An  attempt  has  been  made 
to  prove  that  all  such  astigmia  (and,  in  fact,  that  all  congenital 
astigmia)  occurs  in  connection  with  and  results  from 
faulty  or  asymmetrical  development  of  the  cranium.  While  this 
connection  cannot  be  universally  verified,  we  frequently  observe 
that  a  high  degree  of  astigmia  coexists  with  defective  cranial 
development. 

Change  in  the  Form  of  the  Cornea. — The  cornea 
attains  its  full  growth  at  an  early  age,  about  the  third  year.  In 
accordance  with  this  fact,  keratometric  observations  which  have 
been  repeated  upon  the  same  persons  after  the  lapse  of  a  number 
of  years  show  that  very  little  change  takes  place  in  the  form  of 
the  cornea  after  it  has  attained  its  growth.  Exceptionally,  how- 
ever, measurements  have  revealed  a  decided  asymmetry  in  a  cor- 
nea which  had  previously  been  found  free  from  this  defect. 
Such  change  of  form  may  be  ascribed  to  pressure  upon  the  cornea 
by  the  eyelids,  to  tenotomy  or  advancement  of  an  extra-ocular 
muscle,  or  to  asymmetrical  increase  in  the  size  of  the  eyeball. 

But  the  only  common  cause  of  a  decided  change  in  the  form 
of  the  cornea  is  the  interposition  of  scar-tissue,  either  as  the 
result  of  disease  (suppuration)  or  of  traumatism  (corneal  sec- 
tion). In  the  former  case  the  astigmia  is,  for  the  most  part, 
irregular ;  but  with  this  a  certain  amount  of  regular  astigmia, 
capable  of  correction,  may  also  occur.  A  high  degree  of  regular 
astigmia  is  the  rule  after  corneal  section,  as  in  cataract- 
extraction.  The  alteration  in  curvature  is  greatest  immediately 
after  the  operation,  and  gradually  diminishes,  sometimes  vanish- 
ing entirely.  After  the  lapse  of  six  months  no  further  change  is 
to  be  expected. 

Etiology  of  Lenticular  Astigmia 

We  have  learned  that  the  angle  alpha,  which  measures  the 
tilting  of  the  lens  with  reference  to  the  optic  axis,  usually  extends 
downward  and  outward,  varying  in  the  horizontal  meridian 
between  four  and  seven  degrees,  and  in  the  vertical  meridian 
between    two    and    three    degrees ;    we    have    also    learned    that 


240  Errors  of  Refraction 

this  tilting  produces  only  a  slight  degree  of  astigmia,  and  that  the 
principal  factor  in  the  etiology  of  astigmia  of  the  crystalline  lens 
is  asymmetry  of  its  posterior  surface. 

A  marked  increase  of  lenticular  astigmia  occurring  after 
birth  is  usually  attributed  to  a  partial  dislocation  of  the  lens,  as  the 
result  of  traumatism  or  disease. 

Dynamic  Astigmia. — The  hypothesis  of  dynamic  compen- 
satory astigmia  was  first  announced  by  Dobrozvolsky  in  1868.  In 
this  hypothesis  it  is  assumed  that  by  a  partial  or  asymmetrical  con- 
traction of  the  ciliary  muscle  a  certain  amount  of  astigmia  can 
be  produced  for  the  correction  of  an  opposite  corneal  astigmia. 

As  the  result  of  clinical  and  experimental  observations  many 
other  authorities  were  led  to  accept  the  conclusions  of  Dobrowol- 
sky ;  and  with  the  introduction  into  general  use  of  keratometry 
compensatory  astigmia  was  assigned  by  Javal  as  a  potent  factor 
in  causing  the  discrepancy  between  the  keratometric  record  and 
the  subjective  astigmia. 

Supported  by  these  authorities,  the  hypothesis  has  been 
widely  accepted.  The  amount  of  compensatory  action  which 
has  been  assigned  to  the  ciliary  muscle  varies,  according  to  dif- 
ferent authorities  between  1  D  and  3  D. 

There  must  be  considered,  as  of  the  utmost  importance  in 
reaching  a  correct  conclusion  in  the  study  of  this  subject,  the 
ability  of  the  individual  to  decipher  diffusion-images,  the  inability 
to  discriminate  between  perfectly  sharp  images  and  those  formed 
with  slight  diffusion,  the  stenopaeic  effect  of  partially  closing  the 
lids,  and  the  variation  in  the  size  of  the  pupil,  especially  in  com- 
paring the  tests  of  vision  with  cycloplegia  and  without  it. 

Having  eliminated  these  sources  of  error,  Hess  proceeded 
to  determine  by  experiment  whether  or  not  partial  accommodation 
is  possible.  His  device  consisted  essentially  of  two  cotton 
threads  stretched  at  right  angles  to  each  other.  The  stands  sup- 
porting the  threads  were  movable  along  a  graduated  rod.  The 
astigmia  (natural  or  artificial)  of  the  examinee  being  known, 
the  vertical  thread,  for  instance,  was  placed  at  the  near-point  of 
the  horizonal  meridian  of  the  eye,  while  the  horizontal  thread 
was  placed  at  the  near-point  of  the  vertical  meridian.  By  mov- 
ing one  of  the  threads,  the  power  of  the  eye  to  accommodate  in 
one  meridian  could  be  ascertained.  Having  examined  in  this 
way  twenty-three  individuals,  Hess  found  that  in  no  case  could 


Astigmia  241 

the  highest  possible  partial  contraction  exceed  .37  D,  and  it  was 
often  less  than  .1  D,  that  is,  not  that  this  amount  of  partial  ac- 
commodation actually  existed,  but  that  it  could  not  be  excluded 
by  the  test. 

Although  it  is  possible,  even  probable,  that  contraction  of 
the  ciliary  muscle  may  in  certain  instances  be  more  effective  in 
one  meridian  than  in  another,  yet  the  belief  that  we  are  able  to 
control  this  action  for  the  correction  of  astigmia,  is  in  my  opinion 
wholly  untenable,  for  it  requires  the  highly  improbable  assump- 
tion of  the  existence  of  a  separate  nerve  nucleus  for  each  prin- 
cipal meridian. 

Degree  of  Astigmia 

The  degree  of  regular  astigmia  varies  from  an  inappre- 
ciable amount  to  15  D  or  more.  In  a  few  instances  only  has  an 
amount  reaching  the  latter  degree  (15  D)  of  congenital  astigmia 
been  recorded.  A  very  high  degree  of  astigmia  has  occa- 
sionally been  measured  with  the  keratometer  shortly  after  the 
healing  of  corneal  section,  only  a  minor  portion  of  which,  how- 
ever, is  permanent.  With  the  exception  of  such,  an  amount 
exceeding  6  D  is  of  infrequent  occurrence. 

Donders  and  others  of  the  older  ophthalmologists  regarded 
astigmia  of  less  than  1  D  as  physiological  and  as  not  requiring 
correction;  but  at  the  present  day  .25  D,  or  even  .12  D  is  consid- 
ered sufficient  to  call  for  correction. 

Classifications  of  Astigmia 

Classification  with  Reference  to  the  Position  of  the 
Principal  Meridians. — Since  the  meridian  of  greatest  curva- 
ture of  the  eye  is,  as  a  rule,  vertical  or  nearly  so,  the  astig- 
mia which  results  from  this  kind  of  asymmetry  is  said  to  be 
with  the  rule,  or  direct. 

When,  as  sometimes  is  the  case,  the  meridian  of  greatest 
curvature  is  horizontal,  the  astigmia  is  said  to  be  against  the 
rule,  or  indirect,  or  inverse. 

Corneal  astigmia  is  usually  direct,  the  meridian  of  greatest 
curvature  being  vertical,  or  nearly  so.  Indirect  asymmetry  occurs 
in  young  persons  only  in  about  1.3  per  cent  of  eyes  (Nordenson). 
According  to  Pfals  the  cornea  undergoes  a  gradual  change  from 


242  Errors  of  Refraction 

youth  to  old  age,  so  that  in  the  latter  period  of  life  indirect  cor- 
neal astigmia  is  comparatively  frequent. 

The  astigmia  which  results  from  the  ordinary  corneal  sec- 
tion (upward)  for  cataract-extraction  is  indirect,  since  the  section 
diminishes  the  vertical  curvature  without  materially  altering  the 
horizontal  curvature. 

The  astigmia  which  results  from  the  oblique  position  of  the 
crystalline  lens  is  indirect,  as  is  usually  that  which  results  from 
asymmetry  of  curvature  of  the  lens.* 

Oblique  astigmia  is  that  condition  in  which  the  principal  meri- 
dians are  not  vertical  and  horizontal  (or  nearly  so),  but  make 
angles  of  forty-five  degrees  (approximately)  with  the  vertical  and 
horizontal  lines.  The  distinguishing  limit  between  direct  or  indi- 
rect astigmia  and  oblique  astigmia,  as  thus  defined,  is  arbitrary; 
but  it  is  customary  to  regard  astigmia  as  oblique  when  the 
principal  meridians  are  more  than  twenty  degrees  from  the 
vertical  and  horizontal  lines. 

Classification  with  Reference  to  the  Relative  Direc- 
tions of  the  Principal  Meridians  in  the  Two  Eyes. — In  the 
majority  of  astigmopes  the  defect  is  symmetrical;  that  is,  the 
meridians  of  greatest  and  least  curvature  correspond  in  the  two 
eyes. 

If  the  meridian  of  greatest  curvature  is  vertical  in  one  eye, 
the  probability  is  that  the  meridian  of  greatest  curvature  of  the 
other  eye  is  also  vertical.  So  also,  if  the  upper  extremity  of 
the  meridian  of  greatest  curvature  lies  on  the  temporal  side  of 
the  vertical  meridian  in  the  right  eye,  the  probability  is  that  the 
meridian  of  greatest  curvature  of  the  left  eye  lies  on  the  tem- 
poral side  of  the  vertical  meridian,  and  that  the  angle  of  inclina- 
tion to  the  vertical  meridian  is  the  same,  or  nearly  so,  in  the 
two  eyes. 

We  must  observe,  however,  that  with  the  angular  notation  in 
common  use  in  this  country  the  degree  markings  are  not  the  same 
in  the  two  eyes.  If  the  meridian  of  greatest  curvature  is  de- 
noted by  450  in  the  right  eye,  the  corresponding  marking  for  the 
left  eye  is  1350  (90+45). 

When  the  meridian  of  greatest  curvature  (not  being  vertical 
or    horizontal)    is    marked    by    the    same    angle    (Fig.    86)    in 

•The  astigmia  which  results  from  asymmetry  of  the  posterior  surface  seems  to  be 
invariably  indirect. 


Astigmia  243 

the  two  eyes — that  is,  when  the  meridian  of  greatest  curvature 
is  inclined  towards  the  temple  in  one  eye  and  towards  the  nose 
(to  an  equal  degree)  in  the  other — the  astigmia  is  said  to  be 
asymmetrical  but  homologous. 

When  the  meridians  of  greatest  curvature  in  the  two  eyes 
are  neither  symmetrical  nor  homologous,  as,  for  instance,  when 
one  eye  presents  the  greatest  curvature  in  the  vertical  meridian 
and  the  other  in  the  horizontal  meridian,  the  astigmia  is 
asymmetrical  and  heterologous.  This  kind  of  astigmia  is  of 
comparatively  infrequent  occurrence. 

Classification  with  Reference  to  the  Relation  between 
the  Position  of  the  Retina  and  that  of  the  Focal  Lines. — 
Simple  hyperopic  astigmia  (H  As  or  Ah)  is  that  condition  in 
which,  the  accommodation  being  relaxed,  one  focal  line  falls  upon 
the  retina  while  the  other  lies  behind  it;  or,  it  is  that  condition 
in  which  the  eye  is  emmetropic  in  one  principal  meridian  and 
hyperopic  in  the  other. 

Compound  hyperopic  astigmia  (H  As  Co.  or  H  -\-  Ah) 
is  that  condition  in  which  both  focal  lines  lie  behind  the  retina ;  the 
eye  is  hyperopic  in  both  principal  meridians,  but  more  so  in  one 
than  in  the  other. 

Simple  myopic  astigmia  (M  As  or  Am)  is  that 'condition  in 
which  the  eye  is  emmetropic  in  one  and  myopic  in  the  other 
principal  meridian. 

Compound  myopic  astigmia  (M  As  Co  or  M  -f-  Am) 
is  that  condition  in  which  the  eye  is  myopic  in  both  principal 
meridians,  but  more  so  in  one  than  in  the  other. 

When  in  compound  astigmia  the  hyperopia  or  myopia  is 
relatively  so  great  as  to  outweigh  in  importance  the  astigmia, 
the  condition  is  more  appropriately  designated  as  hyperopia  or 
myopia  with  astigmia. 

Mixed  astigmia  (Ah  -f-  Am)  is  that  condition  in  which  the 
•eye  is  hyperopic  in  one  meridian  and  myopic  in  the  other. 

Since  the  kind  of  astigmia,  in  accordance  with  this  classi- 
fication, depends  upon  the  length  of  the  antero-posterior  diameter 
of  the  eyeball,  it  not  uncommonly  happens  that  compound  hyper- 
opia astigmia  passes  by  degrees  into  simple  hyperopic,  mixed, 
simple  myopic,  and  compound  myopic  astigmia,  with  the  in- 
crease in  diameter  of  the  eye,  as  the  result  of  growth  or  disease. 


244  Errors  of  Refraction 

Symptoms  of  Astigmia 

Of  subjective  symptoms,  subnormal  vision,  asthenopia  and 
headache  are  the  most  characteristic.  These  are,  however,  not 
pathognomonic,  for  each  may  occur  from  some  other  cause. 

Vision  in  Astigmia. — In  the  mildest  grades  of  astig- 
mia vision  may  not  be  below  normal  (6/6),  and  it  may  even 
surpass  this ;  but  in  moderate  and  high-grade  astigmia  vision 
is  always  defective.  The  visual  power  varies,  as  in  other  anom- 
alies, under  different  conditions,  and  especially  with  variation 
in  size  of  the  pupil.  The  latter  is  a  very  important  consideration, 
since  keratometry  shows  that  corneal  asymmetry  and  irregulari- 
ties increase  rapidly  with  increase  of  the  distance  from  the  cor- 
neal summit.  In  this  way  is  explained  the  frequent  manifesta- 
tion of  greater  astigmia  when  the  examination  is  conducted 
under  mydriasis  than  is  shown  without  it. 

The  question  arises  as  to  what  is  the  most  favorable  relation 
between  the  retina  and  the  focal  lines,  that  which  one  will,  as  far 
as  possible,  seek  either  by  exercise  of  accommodation  or  by 
change  in  position  of  the  object  of  vision.  In  answer  to  this 
question,  Javal  has  stated,  as  the  result  of  his  investigations,  that 
an  astigmope  obtains  his  best  vision  when  the  object  is  conjugate 
to  the  retina  in  the  horizontal  meridian;  that  is,  when  the  vertical 
focal  line  falls  upon  the  retina. 

Two  advantages  arise  from  this  relation:  (i)  While  hori- 
zontal lines  are  more  or  less  blurred,  all  vertical  lines  are  distinct ; 
and  experiment  shows  that,  in  reading,  distinctness  of  the  vertical 
strokes  of  the  letters  is  of  more  moment  than  distinctness  of  the 
horizontal  strokes.  (2)  The  object  being  in  focus  in  the  hori- 
zontal meridian,  rays  of  light  which  would  enter  in  the  vertical, 
ametropic  meridian  can  be  largely  excluded  by  partially  closing 
the  lids — a  device  to  which  astigmopes  usually  resort,  and  by 
which  great  improvement  of  vision  is  gained,  especially  if  the 
eye  is  properly  adapted  in  the  horizontal  meridian. 

Reymond  and  others  believe  that  vision  is  preferably  accom- 
plished in  astigmia,  not  as  suggested  by  Javal,  but  by  adapting 
the  eye  first  in  one  and  then  in  the  other  principal  meridian,  and 
that  by  a  rapid  change  in  accommodation  a  composite  mental  im- 
pression is  obtained. 


Astigmia  245 

It  is  possible  that  this  rapid  change  of  accommodation  may 
take  place  under  certain  circumstances ;  in  fact,  it  does  apparently 
occur  when  a  young-  person  affected  with  hyperopic  astigmia  is 
being  examined  with  the  clock-face  chart.  But  that  this  process 
can  be  maintained  for  a  long  period  of  time  as  in  reading,  or 
that  it  can  be  effective  in  high  astigmia  is,  I  think,  entirely 
beyond  the  range  of  probabilities. 

Javal's  theory  is  opposed  also  by  Hess,  who  believes  that  the 
maximum  vision  is  obtained,  not  when  the  eye  is  adapted  in 
either  principal  meridian,  but  when  it  is  so  adapted  that  the  retina 
lies  between  the  two  focal  lines,  at  the  point  where  the  intercepted 
image  is  free  from  distortion  and  zvhere  all  lines  appear  equally 
distinct. 

My  experience  does  not  uphold  the  contention  of  Hess.  I 
find  that  while  the  larger  letters  are  rendered  more  evenly  visible 
by  looking  through  a  lens  which  places  the  retina  in  the  position 
of  least  confusion,  the  smaller  letters  are  less  recognizable  be- 
cause of  the  general  diffusion  than  when  the  vertical  strokes  of 
the  letters  are  distinct. 

The  most  unfavorable  position  of  the  retina  for  reading  is, 
according  to  Javal's  theory,  such  that  the  letters  are  in  focus 
in  the  vertical  meridian.  The  vertical  strokes  of  the  letters  are 
then  blurred  and  the  horizontal  strokes  are  distinct.  Every  point 
of  every  letter  forms  on  the  retina  a  horizontal  line  and  the 
horizontal  diffusion-image  of  one  letter  overlaps  that  of  the  adja- 
cent letter,  so  that  the  reading  of  small,  closely  set  type  is  im- 
possible. 

The  most  favorable  position  of  the  retina — adaptation  in  the 
horizontal  meridian — is  possible  for  distant  vision  only  when  the 
eye  is  emmetropic  in  the  horizontal  meridian  or  hyperopic  with 
sufficient  accommodative  power  to  overcome  the  hyperopia. 

The  most  unfavorable  relation — adaptation  of  the  vertical 
meridian — cannot  be  avoided  in  distant  vision  when  the  eye  is 
emmetropic  in  the  vertical  meridian,  being,  in  the  horizontal 
meridian,  either  myopic  or  hyperopic  without  accommodative 
power  to  render  it  emmetropic  at  the  expense  of  the  vertical 
meridian. 

In  near  vision  the  most  advantageous  adaptation  will  be  ac- 
complished, as  far  as  possible,  by  change  in  position  of  the  object 
and  by  exercise  of  accommodation. 


246  Errors  of  Refraction 

Vision  in  Irregular  Astigmia. — In  pathological  irreg- 
ular astigmia  defective  vision  is  a  constant  and  characteristic 
symptom.  Objects  appear  distorted,  and  sometimes  there  is 
monocular  diplopia  or  polyopia.  The  latter  is  especially  common 
in  irregular  crystalline  astigmia  occurring  as  a  precursor  of 
cataract. 

Double  or  triple  monocular  znsion  is  not  uncommonly  ob- 
served in  ametropia,  disappearing  with  the  correction  of  the 
ametropia  by  a  suitable  lens.  Such  multiple  vision  is  probably 
due  to  slight  difference  in  index  of  the  three  main  segments  of 
the  crystalline  lens,  so  that  each  segment  gives  rise  to  a  separate 
retinal  image  of  an  object.  In  emmetropia  these  images  are  so 
nearly  superposed  that  they  are  fused  as  a  single  image;  but 
when  the  retina  is  remote  from  the  position  of  the  average  focus 
(just  as  in  Schemer's  experiment),  vision  is  multiple.  This  is  a 
frequent  symptom  in  hysterical  spasm  of  the  accommodation 
(Parinaud) . 

Asthenopia. — Astigmopes  more  often  complain  of  asthe- 
nopia than  pf  defective  vision.  This  is  especially  so  as  regards 
the  large  number  of  eye-workers — students,  accountants  and 
artisans — whom  civilization  has  produced.  As  with  other  refrac- 
tive anomalies,  the  asthenopia  bears  no  fixed  relation  to  the  degree 
of  astigmia.  It  depends  rather  upon  the  state  of  health  and 
the  character  of  the  work  pursued. 

Headache  in  astigmia,  as  in  hyperopia,  occurs  usually  in 
conjunction  with  asthenopia,  but  it  sometimes  occurs  without 
other  symptoms  pointing  to  refractive  error. 

Asthenopia  and  headache  occurring  in  hyperopia  are  usually 
ascribed  to  exhaustion  of  the  ciliary  muscle  (accommodative 
asthenopia).  In  myopia  these  symptoms  are  assigned  to  dis- 
turbance in  the  relation  between  accommodation  and  convergence 
(muscular  asthenopia).  In  astigmia  either  or  both  of  these 
kinds  of  asthenopia  may  arise,  but,  doubtless,  the  main  source 
of  disturbance  is  nerve-exhaustion  (retinal  asthenopia)  resulting 
from  the  mental  effort  to  interpret  diffusion-images.  It  is  also 
possible  that  in  oblique  astigmia  asthenopia  may  arise  from  the 
tax  imposed  upon  the  oblique  muscles  in  their  effort  to  obliterate 
distortion  by  rotating  the  meridians  of  the  eye,  as  is  maintained 
by  Savage. 

Objective     Symptoms.— The     pathognomonic     objective 


Astigmia  247 

symptoms  of  astigmia  have  already  been  considered  in  dealing 
with  objective  optometry.  In  addition  to  these  there  are  con- 
junctival congestion  (occurring  especially  after  close  application 
of  the  eyes),  chronic  conjunctivitis,  blepharitis,  and  congestion  of 
the  optic  nerve  and  retina,  all  of  which  occur  also  in  other  con- 
ditions. 

Diagnosis  of  Astigmia 

The  methods  of  measuring  the  degree  of  astigmia  have  been 
given  in  Chapter  X.  The  order  of  applying  these  tests  which 
has  been  recommended  for  other  refractive  errors  may  advan- 
tageously be  followed  also  in  astigmia. 

The  various  reasons  for  the  discrepancy  which  is  liable  to 
be  found  between  the  ophthalmometric  record  and  the  subjective 
error  as  determined  by  the  cylindrical  correcting  lens  have  been 
enumerated  in  Chapter  X.  In  the  practical  determination  of 
the  correcting  lens  there  is  still  another  limitation  to  the  useful- 
ness of  the  ophthalmometer.  This  is  that  it  does  not  reveal  any 
information  as  to  the  refraction  of  the  eye  in  relation  to  the  posi- 
tion of  the  retina.  If,  for  instance,  the  instrument  records 
1  D  of  direct  astigmia,  we  do  not  know  from  this  record 
whether  the  correcting  lens  is  -f-  1  D,  axis  90  or  —  1  D,  axis  180. 
This  question  has  to  be  decided  by  other  tests. 

Of  the  two  other  objective  methods,  ophthalmoscopy  and 
skiascopy,  the  former  is  indispensable  in  that  it  informs  us 
whether  or  not  the  interior  of  the  eye  is  in  a  healthy  condition, 
but  as  a  means  of  measuring  the  degree  of  astigmia  it  has  been 
entirely  supplanted  by  other  tests.  Skiascopy,  which  is  the  most 
practically  valuable  of  the  objective  tests,  is  especially  useful  in 
young  children,  for  it  can  be  applied  with  considerable  accuracy 
at  an  age  when  ophthalmometry  and  subjective  methods  cannot 
be  used. 

After  completion  of  the  objective  examination,  a  careful 
subjective  examination  with  trial  lenses  must  be  conducted.  In 
this  examination  the  indications  for  cycloplegia  are  the  same  as 
in  other  refractive  errors,  for  it  is  to  ascertain  what  degree  of 
hyperopia  or  myopia  is  associated  with  the  astigmia  that  the 
cycloplegic  is  employed. 

We  must  note  any  discrepancy  between  the  astigmia  as  esti- 
mated with  cycloplegia  and  without  it.     The  manifestation  of  a 


248  Errors  of  Refraction 

higher  degree  when  the  pupil  is  dilated  by  the  cycloplegic  usually 
indicates  that  the  asymmetry  is  greater  peripherally  than  near  the 
axis.  Since  in  normal  vision  the  peripheral  portion  of  the  cornea 
is  excluded,  the  estimate  made  without  cycloplegia,  if  corrobo- 
rated by  other  tests,  is  that  which  should  be  adopted  for  the  cor- 
recting lens. 

We  sometimes  also  note  a  slight  difference  in  the  position 
of  the  principal  meridians  as  determined  with  cycloplegia  and 
without  it.  This  difference  is  probably  due  to  irregularity  of  the 
cornea,  but  it  is  possible  that  it  is  due,  as  some  authorities  believe, 
to  an  alteration  in  the  crystalline  astigmia  under  the  influence 
of  the  cycloplegic. 

Treatment  of  Astigmia 

The  treatment  of  regular  astigmia  consists  in  the  correc- 
tion of  the  defect  by  means  of  a  suitable  cylindrical  or  toric  lens. 
In  the  lower  grades  correction  should  embrace  the  entire  error, 
but  in  high  astigmia  total  correction  will  often  not  be  tolerated 
at  first  on  account  of  the  distorting'  property  of  asymmetrical 
lenses.  After  a  partial  correction  has  been  worn  for  some  time 
the  full  correction  may  be  ordered. 

The  annoyance  which  results  from  the  distortive  action  of 
these  lenses  is  usually  of  short  duration  in  young  persons,  but 
elderly  persons  who  have  not  at  an  earlier  age  become  accus- 
tomed to  asymmetrical  lenses  very  often  decline  to  accept  cor- 
rection of  their  astigmia.  This  is  especially  so  if  the  meridians 
are  oblique.  It  is  possible  that,  as  Savage  believes,  the  annoyance 
which  is  so  marked  in  the  correction  of  oblique  astigmia  re- 
sults from  the  effort  of  the  eyes  to  overcome  the  distortion  by 
rotary  action  (torsion)  of  the  eyes. 

The  apparent  distortion  of  objects  by  asymmetrical  lenses 
is  due  partly  to  the  actual  distortion  of  the  retinal  image,  and 
partly  to  the  effect  exerted  by  the  change  in  accommodation  upon 
binocular  visual  perception.  The  former  kind  of  distortion  has 
been  described  in  Chapter  IV.  The  explanation  of  the  latter 
kind  is  the  same  as  that  for  spherical  lenses,  for  which  reference 
may  be  made  to  the  chapter  on  Hyperopia.  Of  the  distorting 
effect  upon  binocular  vision  caused  by  placing  an  asymmetrical 
lens  before  only  one  eye,  or  a  much  stronger  lens  before  one  eye 


Astigmia  249 

than  before  the  other,  mention  will  be  made  in  the  chapter  on 
Anisometropia. 

In  astigmia  of  high  degree  the  correcting  lenses  should  be 
ordered  for  constant  wear,  and  preferably  so  in  all  astigmia 
exceeding  1  D.  When  the  astigmia  is  less  than  1  D  the  cor- 
recting glasses  may  in  favorable  cases  be  used  only  during  near 
work,  while  in  other  cases  asthenopia  will  be  relieved  only  if  the 
glasses  are  worn  constantly. 

In  the  correction  of  astigmia  which  has  been  determined 
with  the  eye  under  the  influence  of  a  cycloplegic  we  must  be 
guided  by  the  same  considerations  as  in  hyperopia.  In  other 
words,  we  must  remember  that  in  a  young  person  accommodative 
action  may  modify  the  relative  position  of  the  retina  and  the 
focus.  Thus  an  eye  which  requires  during  cycloplegia  a  -f  .50  D 
cylinder,  may  require  instead,  after  the  effect  of  the  cycloplegic 
has  worn  off,  a  —  .50  D  cylinder  with  its  axis  at  right  angles  to 
the  axis  of  the  convex  cylinder  which  was  formerly  accepted. 
Or  if  the  correction  under  cycloplegia  is  a  +  i-oo  D  cylinder  it 
may  be  necessary  to  place  before  this  a  —  .50  D  sphere  in  order 
to  afford  clear  vision  after  the  cycloplegic  effect  has  parsed  off. 

We  must  therefore  follow  the  same  general  rule  which  was 
given  for  the  prescription  of  spherical  lenses ;  that  is,  we  must 
select  the  greatest  convexity  or  the  least  concavity  which  is  com- 
patible with  clear  distant  vision. 

Prescription  of  Compound  Lenses. — Since  it  is  the 
duty  of  the  optician  to  provide  lenses  exactly  as  called  for  by 
the  prescription  presented  to  him,  we  must,  in  ordering  correc- 
tion for  hyperopia  or  myopia  associated  with  astigmia,  make 
use  of  the  knowledge  gained  in  the  study  of  asymmetrical  refrac- 
tion, so  that  every  combination  of  lenses  may  be  reduced  to  its 
simplest  form,  or  to  such  other  form  as  we  may  deem  preferable. 

In  our  study  of  this  subject  (Chapter  IV)  we  have  learned 
that  the  same  refractive  effect  can  be  obtained  by  combining  two 
cylinders  at  right  angles  (the  crossed  cylinder),  by  combining  a 
spherical  with  a  cylindrical  lens,  or  by  using  a  toric  lens.  The 
first  of  these  combinations,  the  crossed  cylinder,  has  no  advan- 
tages over  the  other  two,  and  it  is  not  ordinarily  used.  The  sec- 
ond or  sphero-cylindrical  combination  is  that  which  is  most  com- 
monly employed. 


250  Errors  of  Refraction 

In  ordering  sphero-cylindrical  lenses  we  write  the  prescrip- 
tion as  follows : 

R-f2.25sph.-f  1.50  cyl.,  ax.   75. 
L  -f  175  sph.  -f  2.00  cyl.,  ax.  105. 

The  symbol  of  combination  (3)  is  sometimes  placed  be- 
tween the  two  lens  numbers,  but  the  plus  or  minus  sign  is  al) 
that  is  necessary. 

In  combining  lenses  we  should  be  familiar  with  the  principles 
of  transposition.    We  readily  understand,  for  instance,  that 

-f  .50  sph.  —  .50  cyl.,  ax..  180°  =  -f  .50  cyl.,  ax.900 

-f  1. 00  sph.  —  .50  cyl.,  ax.  1800  =  -f  .50  sph.  -f  .50  cyl.,  ax.  900 
—  1. 00  sph.  -f  .75  cyl.,  ax.  1800  =  —  .25  sph.  —  .75  cyl.,  ax.  90° 

In  the  last  two  examples  the  cylinder  has  a  smaller  numerical 
value  than  the  sphere ;  in  such  cases  the  combination  is  equivalent 
to  two  homogeneric  lenses;  that  is.  in  the  simplest  form  the  signs 
of  both  component  lenses  arc  alike;  both  are  plus  or  both  are 
minus. 

Therefore  when  we  have  a  combination  with  unlike  signs,  the 
numerical  value  of  the  cylinder  being  no  greater  than  that  of  the 
sphere,  we  transpose  the  combination  as  follows :  Subtract  the 
numerical  value  of  the  cylinder  from  that  of  the  sphere,  zvhich 
gives  the  value  of  the  new  sphere,  and  change  the  sign  of  the 
cylinder,  with  a  change  of  ninety  degrees  in  its  axis. 

If  we  take  another  series  of  examples  in  which  the  cylindri- 
cal element  is  the  greater,  we  shall  see  that  if  the  lenses  have 
different  signs,  if  the  lenses  are  heterogeneric,  they  remain  so 
after  transposition.     Thus : 

—  i.oosph.  -f  1.50  cyl.,  ax.  900  = -f  .50  sph.  —  1.50  cyl.,  ax.  180 ° 
-f  i.oosph.  —  1.50  cyl.,  ax.  1800  = —  .50  sph. -f  1.50  cyl.,  ax.  900 

—  i.oosph.  +  2.50 cyl.,  ax.  90°  =  -f  1.50 sph.  —  2. 50 cyl.,  ax.  1800 

In  this  series  of  examples  the  lenses  have  been  reduced  to 
a  simpler  form  by  transposition,  except  the  last  combination.  This 
has  been  transposed  from  a  simpler  to  a  less  desirable  form;  that 
is,  from  a  lighter  to  a  heavier  combination. 

Unless  we  have  a  special  reason  for  doing  otherwise,  we 
should  write  our  prescription  for  any  compound  lens  in  its  sim- 
plest form,  because,  while  the  optician  would  probably  have  this 
in  stock,  the  equivalent  lens  in  another  form  would  have  to  be 
specially  ground. 


Astigmia  251 

In  the  simplest  form  of  a  heterogeneric  combination  the 
numerical  value  of  the  spherical  element  is  not  more  than  one- 
half  of  that  of  the  cylinder.  Whenever  the  sphere  exceeds  this 
proportion  we  should  transpose  the  combination  in  the  following 
way: 

Obtain  the  value  of  the  nezv  sphere  by  subtracting  the  nu- 
merical value  of  the  old  sphere  from  that  of  the  cylinder;  change 
the  signs  of  both  sphere  and  cylinder  and  make  a  change  of  ninety 
degrees  in  the  axis  of  the  cylinder. 

Prescription  of  Toric  Lenses. — In  ordering  toric  lenses  we 
may  write  the  prescription  in  the  ordinary  way,  as  a  sphero- 
cylinder  and  add  the  word,  "Toric."  The  optician  will  then  make 
the  necessary  transposition.  If  we  deem  it  advisable  we  may  also 
specify  the  degree  of  concavity  which  we  desire  for  its  peri- 
scopic  effect. 

Toric  lenses  are  usually  made  on  a  base  curve  of  6  D,  more 
rarely  on  a  curve  of  3  D  or  9  D.  Thus  a  plano-toric  convex  lens 
of  2  D  of  asymmetry,  made  on  a  6  D  curve,  would  have  a  curve 
of  -f-  6  D  in  one  meridian  and  of  -f-  8  D  in  the  other. 

Suppose  that  we  have  a  case  of  simple  hyperopic  astigmia 
for  which  we  wish  to  order  a  toric  correction.  The  6  D  curve  is 
selected  and  a  concavity  of  —  6  D  (spherical)  is  ground  on  the 
inner  face  of  the  proper  plano-toric  lens. 

But  if  in  addition  to  the  2  D  of  astigmia  there  is  4  D  of 
hyperopia  we  should  have  only  —  2D  for  the  periscopic  effect. 
If  this  is  not  deemed  sufficient,  the  9  D  curve  should  be 
selected,  which  would  give  —  5  D  for  the  periscopic  effect. 

Surgical  Treatment  of  Astigmia. — It  has  been  proposed 
to  overcome  regular  astigmia  by  surgical  means — by  corneal  in- 
cisions made  at  right  angles  to  the  meridian  of  greatest  curvature. 
But  the  impossibility  of  regulating  the  result  renders  it  improbable 
that  this  method  will  come  into  practical  use. 

The  following  authorities  have  been  consulted  in  the  prep 
aration  of  the  foregoing  chapter : 


/ 


Young,  Mechanism  of  the  Eye. 
Airy,   On   a  Peculiar  Defect  in   the  Eye  and  a  Mode   of 
Correcting  It,  Trans.  Camb.  Philos.  Soc,  Vol.  II,  1827 
Mackenzie,  Diseases  of  the  Eye. 


252  Errors  of  Refraction 

Burnett,  Treatise  on  Astigmatism;  and  Astigmia  or  Astig- 
matism, Which?  Am.  Jour.  Ophth.,  1903. 

Donders,  Anomalies  of  Refraction  and  Accommodation. 

Helmholtz,  Optique  Physiologiquc. 

Knapp,  Die  Kriimmung  der  Hornhaut  des  Menschlichen 
Auges;  und  Uebcr  die  Asymmetrie  des  Auges,  &c,  Arch,  fur 
Ophth...  1 861. 

Landolt,  Refraction  and  Accommodation  of  the  Bye;  and 
Relations  Between  the  Conformation  of  the  Cranium  and  That  of 
the  Eye,' Brit.  Med.  Jour.,  1881. 

De  Wecker,  C.  R.  de  la  Soc.  d' Anthropologic  de  Paris,  1868. 

Xordenson,  Recherches  Ophtalmomctriques,  .  Memories 
d'Ophtalmometrie. 

Pfalz,  Perverse  Astigmatism,  Report  of  Ninth  Int.  Cong,  of 
Ophth.,  Arch,  of  Ophth.,  1899. 

Tscherning,  Physiologic  Optics. 

Dobrowolsky,  Ueber  verschiedene  Veranderungen  des  Astig- 
matismus  unter  dem  Einflusse  der  Accommodation,  Arch,  fur 
Ophth.,  1868;  also  Annal.  d'Oculistique,  1869. 

Gradle,  Zur  Correction  des  Astigmatismus  durch  Ingleich- 
massige  Anspannung  des  C Mar  musk  els,  Arch,  fur  Ophth.,  1897. 

Bull,  Du  Rapport  de  la  Contraction  Irregulicre  du  Muscle 
Ciliare  Avec  Astigmatisrnc,  Annal.  d'Oculistique,  1892. 

Javal,  Memoires  d'Ophtahnomctrie,  and  Note  sur  le  Choix 
des  Verres  Cylindriqucs,  Annal.  d'Oculistique,  1865. 

Hess,  Arbeitcn  aus  dem  Gebiete  der  Accommodationslehre , 
Arch,  fur  Ophth.,  1896;  and  Uebcr  das  Vorkommen  Partieller 
Ciliarmuskel  Contraction,  Arch  fiir  Ophth.,  1897. 

Reymond,  Sulla  Vision e  Veil'  Astigmatismo,  Annal,  d'Ottal., 
XVI ;  and  Festschrift,  von  Helmholtz. 

Parinaud,  Ocidar  Manifestations  of  Hysteria,  Norris  and 
Oliver's  System  of  Diseases  of  the  Eye. 

Savage,  Ophthalmic  Myology. 

Bates,  A  Suggestion  of  an  Operation  to  Correct  Astigmatism, 
rch.  of  Ophth.,  1894. 

Pfliiger,  Traitment  Operatoire  de  I ' Astigmatisme ;  Annal. 
Nilistique,   1896. 

,  nngst,  Corneal  Measurements  after  Extraction  of  Cataract, 
rch-  f  Ophth,  1896. 


CHAPTER  XIV 


ANISOMETROPIA 

We  have  learned  that  a  variation  of  I  D  in  the  refraction 
of  the  eye  corresponds  to  the  minute  variation  of  about  one-sixth 
of  a  millimeter  in  the  radius  of  the  cornea,  or  to  a  variation  of 
one-third  of  a  millimeter  in  axial  length.  It  is  not  surprising, 
therefore,  that  the  refraction  of  one  eye  so  frequently  differs 
from  that  of  the  other  eye.  It  is,  in  fact,  more  surprising  that 
any  one  has  exactly  the  same  refractive  condition  in  the  two  eyes. 
Yet  in  many  persons  there  is  no  difference  which  can  be  detected 
by  the  means  of  examination  at  our  disposal.  This  ideal  condi- 
tion is  called  isomctropia* 

In  a  large  proportion  of  persons  there  is,  however,  an  appre- 
ciable difference  of  refraction  in  the  two  eyes.  This  condition  is 
called  anisometropia. 

While  isometropia  is  the  standard  or  ideal  condition,  as  is 
emmetropia,  and  as  slight  deviation  from  emmetropia  does  not 
constitute  a  real  anomaly,  so  slight  anisometropia  is  not  to  be 
regarded  as  a  pathological  state.  In  other  words,  anisometropia 
is  a  defect  only  when  it  is  sufficient  to  cause  some  disturbance, 
either  visual  or  nervous.  The  least  refractive  difference  which 
we  may  regard  as  constituting  an  anomaly  varies  with  the  refrac- 
tion in  the  two  eyes.  For  instance,  if  one  eye  is  emmetropic  while 
the  other  has  2  D  of  myopia,  there  should  be  no  hesitation  in 
classing  the  anisometropia  as  a  defect,  capable  of  giving  rise  to 
very  great  disturbance ;  but  if  one  eye  has  9  D  and  the  other  1 1  D 
of  myopia  the  same  anisometropia  (2D)  is  a  subordinate  factor. 

Anisometropia  signifies  nothing  as  to  the  state  of  refraction 
in  either  eye.     One  eye  may  be  emmetropic  and  the  other  hype; 
opic  or  myopic ;  one  eye  may  be   hyperopic  and  other   myo| 
(antimctropia)  ;  both  eyes  may  be  hyperopic  or  myopic,  the  de^ 
of  error  not  being  the  same  in  the  two  eyes ;  or  one  eye  maj 

'From  fcos,  equal;  JMTpov,  measure  ;  and  »4*>  sight. 

253 


254  Errors  of  Refraction 

astigmopic,  or  there  may  be  a  greater  degree  of  astigmia  in 
one  eye  than  in  the  other. 

Etiology. — Anisometropia  may  be  either  congenital  or  ac- 
quired, being  more  frequently  congenital  and  due  to  defective 
development  of  one  eye,  with  or  without  involvement  of  the  corre- 
sponding half  of  the  cranium.  Acquired  anisometropia  results 
from  removal  or  luxation  of  the  crystalline  lens ;  from  alteration 
of  corneal  curvature,  produced  by  ulceration  or  corneal  section; 
from  elevation  of  the  retina  in  partial  detachment ;  or  from  un- 
equal post-natal  increase  in  size  of  the  eye,  as  from  progressive 
myopia. 

Vision  in  Anisometropia. — Vision  in  anisometropia  may 
be  accomplished  in  one  of  the  three  following  ways :  ( i )  There 
may  be  binocular  vision;  (2)  vision  may  be  monocular,  either  eye 
being  used  alternately;  or  (3)  vision  may  be  monocular,  one  eye 
being  used  to  the  exclusion  of  the  other. 

Binocular  Vision  in  Anisometropia. — It  having  been  ascer- 
tained by  means  of  the  stereoscope  or  otherwise  that  an 
anisometrope  possesses  binocular  vision,  the  question  arises  as  to 
the  manner  in  which  such  vision  is  accomplished ;  whether  by 
exercising  a  greater  amount  of  accommodation  in  one  eye  than  in 
the  other,  or  by  the  mental  fusion  of  the  clear  image  as  formed  in 
the  adapted  eye  with  the  blurred  image  as  formed  in  the  other. 
The  latter  and  commonly  accepted  view  was  disputed  in  1889  by 
Fick,  who  cited  a  number  of  cases  in  evidence  of  his  opinion  that 
the  refraction  is  equalized  by  unequal  action  of  the  ciliary  muscle. 
This  theory,  which  has  also  been  advocated  by  Schneller,  is 
opposed  by  Hess,  who  from  a  number  of  experiments  concludes 
that  there  is  no  evidence  in  favor  of  unequal  accommodation  in 
the  two  eyes.  This  question  is  similar  to  that  of  dynamic  com- 
pensatory astigmia.  We  have  no  reason  to  believe  that  the 
ciliary  muscle  of  one  eye  can  be  innervated  alone,  or  that  when 
both  muscles  are  innervated,  one  can  receive  a  designedly  greater 
impulse  than  the  other.* 

Alternate  Vision  in  Anisometropia. — This  generally 
occurs  when  one  eye  is  emmetropic  or  nearly  so,  the  other  eye 


*It  may  happen,  however,  from  an  unequal  receptivity  (irritability)  of  the  ciliary 
muscles  that  stimulation  of  the  accommodation-center  may  give  rise  to  greater  contrac- 
tion of  the  muscle  in  one  eye  than  in  the  other,  as  is  artificially  effected  by  the  in- 
stillation of  eserin  in  one  eye.  Similarly,  it  may  be  possible  that  because  of  unequal 
sclerosis  the  same  impulse  may  produce  a  greater  change  in  curvature  of  the  lens  in 
one   eye   than   in   the   other. 


Anisometropia  255 

having  3  D  or  4  D  of  myopia,  and  both  eyes  having  good  visual 
acuity.  Though  deprived  of  stereoscopic  vision,  the  anisometrope 
who  sees  in  this  way  enjoys  a  certain  advantage,  in  that  he  has 
good  distant  vision  and  yet  does  not  require  reading  glasses,  even 
though  he  may  have  passed  the  presbyopic  age,  since  the  emme- 
tropic eye  serves  for  distant  and  the  myopic  eye  for  near  vision. 

Monocular  Vision  with  Permanent  Exclusion  of  One 
Eye. — Vision  is  accomplished  in  this  way  usually  when,  in 
addition  to  the  anisometropia,  one  eye  is  materially  below  its 
fellow  in  visual  power.  Strabismus,  either  convergent  or  diver- 
gent, is  the  common  accompaniment  of  this  condition,  convergence 
being  of  more  frequent  occurrence  in  hyperopia,  while  divergence 
is  the  usual  condition  in  myopia. 

Anisometropia  Asthenopia. — Since  any  kind  of  refrac- 
tive error  is  capable  of  giving  rise  to  asthenopia,  it  is  ordinarily 
impossible  to  discriminate  between  asthenopia  due  to  this  cause 
and  that  which  is  directly  referable  to  the  inequality  of  refraction 
in  the  two  eyes ;  but  that  this  inequality  is  of  itself  capable  of 
producing  asthenopia  is  attested  by  occurrence  of  the  latter  in 
cases  in  which  one  eye  is  emmetropic  and  the  other  slightly  myopic 
if  there  is  binocular  vision,  while  no  such  symptoms  occur  if  the 
emmetropic  eye  is  used  for  distance  and  the  myopic  eye  for  near 
work. 

Anisometropia  asthenopia  is  due  to  nerve  exhaustion  in  the 
effort  to  maintain  binocular  vision  under  disadvantageous  condi- 
tions. Not  only  is  there  indistinctness  of  images  in  the  unadapted 
eye,  but  the  images  in  the  two  eyes  are  unequal  in  size.  This 
inequality  may  be  slight  and  due  chiefly  to  the  diffusion  on  the 
retina  of  the  light  in  the  unadapted  eye,  or  the  inequality  may  be 
very  great,  as  when  one  eye  has  been  rendered  aphakic  by  the 
removal  of  its  cataractous  lens. 

When  anisometropia  has  existed  since  birth,  the  eyes  may 
never  have  learned  binocular  vision,  one  eye  having  passed  into  a 
state  of  strabismus  at  an  early  age ;  or,  if  binocular  vision  exists, 
the  nervous  mechanism  may  have  become  adapted,  by  training,  to 
the  inequality  of  images.  But  even  in  this  most  favorable  condi- 
tion asthenopia  may  arise  at  any  time,  as  when  a  special  tax  is 
thrown  upon  the  eyes,  or  when  the  bodily  vigor  is  reduced  from 
any  cause. 

Treatment. — In   the  majority  of   eyes   which   require   the 


256 


Errors  of  Refraction 


services  of  the  refractionist  the  ametropia  of  one  eye  will  be 
found  to  differ  slightly  from  that  of  the  other  eye.  In  all  such 
cases  the  correction  appropriate  for  each  eye  should  be  ordered. 
It  should  be  our  aim  also  to  give  the  appropriate  correction  for 
each  eye  and  thus  to  restore  the  normal  relationship  when  the 
dissimilarity  is  more  marked ;  but,  unfortunately,  many  persons 
will  not  tolerate  such  correction. 

The  explanation  of  this  intolerance  is  found  partly  in  the 
nerve-disturbance  produced  when  an  eye  which  has  previously 
acted  only  a  subordinate  part  in  vision  is  suddenly  put  in  condition 
to  co-act  with  its  fellow,  and  partly  in  the  secondary  effects  of 
lenses,  such  as  have  been  described  in  previous  chapters.  In  axial 
ametropia  a  lens  worn  at  the  anterior  focus  of  the  eye  produces 
a  retinal  image  equal  in  size  to  that  formed  in  emmetropia ;  hence 
if  both  eyes  are  properly  corrected,  the  images  in  the  two  eyes 
should  be  of  equal  size.  The  disturbance  cannot,  therefore,  be 
produced  in  this  case  by  unequal  images ;  it  is  due  to  the  change 
from  the  condition  to  which  the  person  has  become  accustomed 
by  lifelong  association. 

In  astigmia  the  proportions  of  the  retinal  image  are 
changed  by  the  correcting  lens,  but  the  image  cannot  be  made 


FIG.     105 


FIG.    I06 


to  conform  to  that  in  the  emmetropic  eye ;  hence,  in  monocular 
astigmia  a  double  difficulty  must  be  overcome  when  the  cor- 
recting lens  is  applied. 

The  apparent  alteration  in  the  size  of  an  object,  which  has 
been  previously  explained  (p.  211),  produces  in  anisometropia  a 
one-sided  disturbance.  This  is  sometimes  a  source  of  great 
annoyance  to  persons  (architects,  mechanics,  etc.)  who  have  to 
deal  with  the  rectangular  form  of  objects.  If  a  rectangular 
diagram,  such  as  is  illustrated  in  Fig.  105,  is  placed  in  front  of 
and  equidistant  from  the  two  eyes  and  viewed  binocularly  with  a 
convex  spherical  lens  before  the  right  eye,  the  rectangular  form  of 


Anisometropia  257 

the  object  will  be  lost,  the  right  side  appearing  broader  than  the 
left,  as  illustrated  in  Fig.  106.  If  a  concave  lens  is  substituted  for 
the  convex  lens,  the  right  side  of  the  figure  appears  smaller  than 
the  left.  This  illusion  arises  from  the  fact  that  the  right  eye  is 
chiefly  concerned  in  looking  at  the  right  side  of  the  object,  while 
the  left  eye  is  the  more  important  as  regards  the  left  side  of  the 
figure.  But  that  the  actual  change  in  size  of  the  retinal  image  is 
not  the  sole  cause  of  this  phenomenon  is  shown  by  the  substitution 
of  a  cylindrical  for  the  spherical  lens.  A  cylindrical  lens,  having 
its  axis  vertical,  produces  the  same  effect  as  the  corresponding 
spherical  lens,  and,  in  this  case  there  is  no  vertical  alteration  of  the 
image.  Hence  we  must  conclude  that  the  apparent  alteration  is 
due  to  disturbance  of  accommodation.  The  effort  of  accommoda- 
tion which  adjusts  the  naked  eye  for  the  left  side  of  the  figure  is 
more  than  sufficient  for  the  right  eye.  which  has  a  convex  lens 
before  it ;  consequently,  the  impression  is  received  that  the  right 
side  is  farther  away  and  larger  than  the  left  side.  Similarly,  with 
the  concave  lens  before  the  right  eye  the  right  side  of  the  figure 
seems  to  be  nearer  and  smaller  than  the  left  side.  The  peculiar 
effect  of  the  cylindrical  lens  is  also  explained  partly  by  the  influ- 
ence which  it  exerts  over  accommodation  and  partly  by  the  actual 
distortion  of  the  image  on  the  retina. 

In  addition  to  the  foregoing  considerations,  the  prismatic 
action  of  lenses  is  an  important  factor  in  the  correction  of  aniso- 
metropia. This  action  is  a  not  uncommon  cause  of  confusion  in 
isometropia,  and  much  more  so  must  it  be  when,  as  in  aniso- 
metropia, the  prismatic  deviation  does  not  correspond  in  the  two 
eyes. 

All  these  difficulties  apply  in  anisometropes  who  have  been 
accustomed  to  binocular  vision  without  lenses.  It  is  far  more 
difficult  to  institute  binocular  vision  in  those  who  have  contracted 
the  habit  of  excluding  one  eye.  In  the  vast  majority  of  such 
cases  it  is  impossible,  except  at  an  early  age,  to  secure  binocular 
vision,  and  especially  is  this  true  when  one  eye  is  used  for  distant 
and  the  other  for  near  vision. 

When  anisometropia  results  from  removal  of  cataract  from 
one  eye  while  the  other  eye  has  good  vision,  the  aphakic  eye  may 
be  of  great  service  in  extending  the  field  of  vision  and  even  in 
entering  subordinately  into  binocular  vision ;  but  very  rarely  will 
such  an  eye  accept  correction  by  a  strong  convex  lens.     This  is  at 


258  Errors  of  Refraction 

least  partly  due  to  the  difficulty  of  avoiding  diplopia  which  tends 
to  result  from  the  one-sided  prismatic  deviation. 

The  student  will  already  have  concluded  that  the  treatment 
of  anisometropia  is  attended  with  much  difficulty  and  uncertainty. 
The  course  to  be  pursued  must  in  every  case  be  adapted  to  the 
age  and  condition  of  the  patient.  Childhood  is  the  most  favorable 
age.  By  the  correction  of  the  refractive  error  of  each  eye  in 
young  children,  many  eyes  which  would  otherwise  become  useless 
are  trained  to  perform  their  part  in  binocular  vision.  If  strabis- 
mus and  inferior  visual  acuteness  are  also  present,  the  eye  should 
be  aided  by  stereoscopic  or  other  exercises. 

In  young  adults  having  binocular  vision  with  anisometropia, 
the  first  attempt  should  be  to  equalize  the  refraction,  and  especially 
if  asthenopic  symptoms  are  present  which  are  referable  to  the 
anisometropia.  If  such  correction  is  not  accepted,  the  symptoms 
may  perhaps  be  relieved  by  partial  equalization. 

It  may  be  stated,  as  a  general  rule,  that  in  persons  who  have 
reached  the  presbyopic  age  without  equalization  of  refraction  the 
correction  of  anisometropia  (except  in  the  lowest  degrees)  will 
not  be  tolerated,  and  this,  whether  the  glasses  are  for  distant  or 
for  near  use. 

The  correction  of  anisometropia  without  binocular  vision  in 
adults  will  almost  invariably  be  a  thankless  task. 

The  following  authorities  have  been  consulted  in  the  prepara- 
tion of  the  foregoing  chapter: 

Donders,  Anomalies  of  Refraction  and  Accommodation. 

Landolt,  Refraction  and  Accommodation  of  the  Eye. 

Fick,  Ueber  ungleiche  Accommodation  bei  Gesunden  und  Ani- 
sometropia, Arch,  fur  Augenheilkunde,  xix,  and  xxxi;  and  Arch, 
fiir  Ophthal.,  xxxv  and  xxxvii. 

Schneller,  Zur  Lchre  von  den  dem  zusammenschen  mit  beiden 
Augendrenenden  Bewegungen,  Arch,  fiir  Ophthal.,  1892. 

Hess,  Versuche  ilber  die  ungebliche  ungleiche  Accommoda- 
tion, &c,  Arch,  fiir  Ophthal.,  1889  and  1892. 

Wadsworth,  Effect  of  a  Cyl.  Lens  with  Vertical  Axis,  &c. 
Trans.  Am.  Oph.  Soc,  1875. 

Lippincott,  Binocular  Metamorphopsia,  Arch,  of  Oph.,  1889. 

Green,  Stereoscopic  Illusions,  &c.  Trans.  Am.  Ophth.  Soc., 
1889. 


CHAPTER  XV 


PRESBYOPIA   AND   ANOMALIES   OF   ACCOMMO- 
DATION 

Since  the  accommodative  power  undergoes  a  gradual  diminu- 
tion with  advancing  years,  there  comes  a  time  when  the  amplitude 
is  not  sufficient  for  the  reading  of  small  print  or  for  the  examina- 
tion of  small  objects  which  must  be  held  near  the  eyes.  We  do 
not  often  hold  our  work  nearer  than  33  cm  (13  inches).  Use  of 
the  eyes  at  this  distance  requires  3  D  of  accommodation,  and  as 
we  can  use  continuously  only  about  two-thirds  of  the  amplitude, 
we  must  have  4.5  D  of  accommodation  in  order  to  be  able  to 
maintain  comfortable  vision  at  a  distance  of  33  cm. 

With  4.5  D  of  accommodation  distinct  vision  is  possible  for 
a  short  time  at  22  cm  (9  inches),  and  a  point  at  this  distance  was 
taken  by  Bonders  as  the  critical  point  in  the  determination  of 
presbyopia.  If  the  amplitude  is  not  sufficient  for  distinct  vision 
at  22  cm  when  any  existing  ametropia  is  corrected,  and  if  the  defi- 
ciency is  due  to  the  physiological  sclerosis  of  the  crystalline  lens, 
the  eye  is  affected  with  presbyopia. 

The  inability  of  the  old  man  (irpesPtJTtis)  to  see  nearby 
objects  clearly  was  described  by  Aristotle,  but  he  was  unable  to 
explain  the  nature  of  this  condition,  which,  indeed,  was  not  fully 
understood  until  after  the  elucidation  of  ocular  refraction  by 
Bonders. 

Age  at  Which  Presbyopia  Occurs. — Reference  to  the 
table  (p.  139)  shows  that  the  age  of  forty  years  is  that  at  which 
the  failing  accommodative  power  reaches  the  limit  of  amplitude 
compatible  with  close  application  of  the  eyes.  Shortly  after  this 
age — almost  always  before  the  forty-fifth  year — the  onset  of  pres- 
byopia occurs. 

Symptoms. — The  most  characteristic  symptoms  of  pres- 
byopia are  a  disposition  to  hold  the  book  or  other  work  a^-  too 
great  a  distance,  asthenopia,  and,  in  neglected  cases,  congestion 
or  inflammation  of  the  conjunctiva. 

259 


260  Errors  of  Refraction 

Diagnosis. — The  diagnosis  of  presbyopia  may  ordinarily  be 
made  without  difficulty,  in  accordance  with  the  age  and  the  in- 
ability to  read  fine  print.  The  static  refraction  must  be  first 
corrected.  If  the  eye  is  myopic,  presbyopia  may  coexist  with  good 
near  vision.  Hyperopia  and  astigmia,  on  the  other  hand,  must 
be  excluded  in  those  cases  in  which  distinct  vision  is  not 
possible  at  22  cm. 

We  must  also  distinguish  between  insufficient  accommodation 
resulting  from  the  physiological  sclerosis  of  the  lens  and  that 
which  is  due  to  weakness  (paresis)  or  paralysis  of  the  ciliary 
muscle. 

Jaeger's  Test  Types  for  Determining  the  Amplitude  of 
Accommodation. — As  Snellen's  test  letters  have  gained  uni- 
versal recognition  for  the  determination  of  distant  visual  acuteness 
so  the  test  cards  of  Jaeger  are  everywhere  in  use  for  testing  near 
vision.  These  cards  consist  of  selections  of  reading  matter  printed 
in  types  of  various  sizes.  No.  1,  being  the  smallest,  is  intended  to 
be  read  at  22  cm  or  less.  If  distant  vision  is  normal  while  this 
print  cannot  be  read  at  the  prescribed  distance — with  the  distance 
correction  if  the  eye  is  ametropic — deficiency  of  accommodative 
power  for  near  work  is  demonstrated.  The  larger  types  are  in- 
tended for  those  who  from  failure  of  accommodation  or  from 
other  causes  cannot  read  the  smallest  print.  The  nearest  point 
at  which  the  smallest  distinguishable  type  can  be  clearly  seen  is 
the  punctum  proximum  (p.p.)  or  near  point  of  the  eye.  The 
distance  of  this  point  from  the  eye  measures  the  amplitude  of 
accommodation. 

Oliver's  Test  Letters. — While  well  adapted  for  the  pur- 
pose for  which  they  were  intended,  Jaeger's  test  types  are  not 
based  upon  the  visual  angle  principle,  as  are  those  of  Snellen.  To 
meet  this  deficiency  Oliver  has  constructed  test  letters  for  near 
vision  in  conformity  with  this  principle. 

Treatment. — The  age  at  which  persons  seek  relief  from 
presbyopia  varies  with  the  individual  accommodative  amplitude 
and  with  the  character  of  the  work  pursued.  The  average  age 
may  be  placed  at  the  forty-fifth  year.  At  this  age  a  convex 
spherical  lens  of  1  D  is  the  probable  correction  which  will  be  re- 
quired. Emmetropes  whose  work  necessitates  continuous  eye- 
strain may  feel  the  need  of  assistance  in  near  work  at  an  earlier 
age — at  any  time  after  the  fortieth  year. 


Presbyopia  and  Anomalies  of  Accommodation  261 

The  average  amount  of  accommodation  possessed  by  healthy 
persons  between  the  ages  of  forty  and  seventy-five  years  and  the 
probable  strength  of  lens  for  adapting  the  eye  for  continuous  near 
work  at  a  distance  of  33  cm  is  indicated  in  the  following  table : 

Age 40         45  50  55  &°  65  70        75 

Accom 4.5  D.    3.5  D.    2.5  D.     1.75  D.     1     D.    0.75  D.    0.25  D.    0 

Lens     1  2  2.75  3-25         3-5  3-5  3-5 

Although  this  table  serves  as  a  guide,  it  is  not  to  be  blindly 
followed  in  individual  cases.  The  appropriate  lens  must  be  selected 
in  each  case  in  accordance  with  the  amplitude  of  accommodation 
and  the  distance  for  which  it  is  desirable  that  the  eyes  may  be 
adapted. 

When  there  is  normal  visual  acuteness  we  seldom  find  it 
necessary  to  prescribe  a  stronger  presbyopic  correction  than  2.50 
D,  or  2.75  D,  since  in  ordinary  reading  and  in  desk  work  the  full 
amplitude,  as  estimated  by  Donders,  is  not  required,  and  since  a 
stronger  correction  would  entail  blurred  vision  at  the  distance  of 
ordinary  use.  Sometimes,  however,  we  are  called  upon  to  order 
the  full  presbyopic  correction  for  persons  who  are  engaged  in  very 
exacting  near  work,  and  also  for  persons  whose  visual  acuity  is 
below  the  normal  standard. 

It  is  apparent  that  as  the  strength  of  the  presbyopic  lens  is 
increased  the  range  of  vision  is  diminished,  since  the  lenses  have 


fig.  107 

the  effect  of  producing  an  artificial  myopia,  greatly  to  the  detri- 
ment of  distant  vision.  On  this  account  elderly  people  usually 
acquire  the  habit  of  wearing  their  near-glasses  far  down  on  the 
nose,  so  that  they  may  look  above  them  during  distant  vision.  A 
convenient  form  of  glass,  sometimes  preferred  by  business  men 
and  public  speakers  is  that  known  as  the  clerical  lens  (Fig.  107), 
which  has  the  upper  portion  cut  away. 


262  Errors  of  Refraction 

Bifocal  Lenses. — Ametropes  who  require  glasses  for  distance 
and  other  glasses  for  near  use  often  find  convenience  in  the  use 
of  bifocal  glasses. 

The  original  split  bifocal  or  Franklin  lenses  consist  of  two 
lenses,  each  properly  centered,  and  separated  by  a  horizontal  line 
(Fig.  108).  The  upper  lens  is  for  distant  and  the  lower  lens  for 
near  vision.  Because  of  the  too  restricted  field  of  view  for 
distance,  Franklin's  invention  has  been  modified  by  making  the 
dividing  line  curved  (Fig.  109). 

Although  bifocal  glasses  may  be  made  in  a  number  of 
different  ways,  at  the  present  time  there  are  only  two  kinds  of 
such  glasses  in  common  use.  These  are:  (1)  the  cemented  bifo- 
cal, in  which  the  presbyopic  correction  is  cemented  to  the  lower 
part  of  the  distance  glass;  and  (2)  the  fused  or  invisible  bifocal, 


fig.  109 

in  which  the  presbyopic  correction  of  flint  glass  is  embedded  in  a 
concavity  made  in  the  distance  glass  of  lower  index,  the  two  being 
fused  into  a  solid  piece.  In  making  these  fused  bifocals  great 
care  has  to  be  exercised  to  prevent  marring  of  the  curvatures 
during  the  process  of  fusion.  If  properly  made,  they  are  the 
most  satisfactory  glasses  possible  for  the  ametropic  presbyope. 

Spasm  of  Accommodation 

Owing  to  the  extreme  ease  of  accommodative  changes  in 
childhood,  there  is  in  almost  all  young  hyperopes  a  diminution  of 
the  hyperopia  effected  by  action  of  the  ciliary  muscle.  So 
accustomed  is  the  young  hyperope  to  exercise  this  accommodation 
that  he  will  be  unable  totally  to  relax  it  when  the  correcting  lens 
is  placed  before  his  eye.  A  certain  amount  of  unrelaxable  accom- 
modation is  physiological,  being  due  to  the  tone  of  the  ciliary 


Presbyopia  and  Anomalies  of  Accommodation  263 

muscle.  The  tone  of  the  muscle  keeps  it  in  a  state  of  slight  con- 
traction. Hence,  even  in  adults  the  refractive  power  of  an  eye  is 
slightly  less  when  tested  under  cycloplegia  than  it  is  when  the  eye 
is  in  its  normal  condition. 

The  increase  of  refraction  arising  from  physiological  tone 
of  the  ciliary  muscle  may  vary  from  .25  D  to  .50  D  in  the  adult 
to  1  D  or  more  in  childhood. 

Not  infrequently  in  childhood  and  early  adult  life  the  action 
of  the  extremely  excitable  ciliary  muscle  transcends  the  physio- 
logical limit,  and  a  condition  of  cramp  or  spasm  of  accommodation 
results.  In  this  state  an  existing  hyperopia  may  be  overcorrected 
with  the  production  of  an  apparent  myopia. 

The  effort  to  overcome  hyperopia  is  not,  however,  the  only 
cause  of  accommodative  spasm.  This  may  be  attributed  to  astig- 
mia,  myopia,  overuse  of  the  eyes,  insufficiency  of  convergence, 
hysteria,  and  to  irritation  from  the  local  application  of  certain 
drugs   (miotics),  such  as  eserin  and  pilocarpin. 

Symptoms. — The  symptoms  which,  when  taken  in  conjunc- 
tion with  the  age  (childhood  and  early  adult  life),  are  charac- 
teristic of  accommodative  spasm  are  inability  to  see  clearly  at  a 
distance,  asthenopia,  headache,  macropsia  and  monocular  polyopia. 

Macropsia. — In  accommodative  spasm  a  very  slight  impulse 
produces  an  inordinately  great  accommodative  action,  and  in  order 
to  adapt  the  eye  for  a  certain  distance,  a  much  slighter  innervation 
of  the  accommodative  center  is  requisite  than  under  normal  con- 
ditions. Because  of  this  unnaturally  slight  effort  of  accommo- 
dation, objects  are  supposed  to  be  farther  away  and  consequently 
larger  than  they  really  are.  Since  the  size  of  an  object 
is  judged  in  accordance  with  previous  experience,  macropsia 
occurs  only  in  recently  acquired  spasm,  such  as  is  occasionally 
manifested  in  hysteria  {hysterical  amblyopia),  or  such  as  is  pro- 
duced by  the  instillation  of  a  miotic. 

Monocular  Polyopia. — This  symptom  has  already  been 
mentioned  as  occurring  in  ametropia.  The  same  explanation 
serves  to  explain  the  polyopia  which  occurs  in  accommodative 
spasm,  since  in  this  condition  the  eye  is  rendered  myopic  by  the 
excessive  action  of  the  accommodation. 

Diagnosis. — The  diagnosis  of  accommodative  spasm  is 
made  in  accordance  with  the  above-mentioned  characteristics,  cor- 
roborated by  determination  of  the  true  refractive  condition  with 


264  Errors  of  Refraction 

the  aid  of  atropin-cycloplegia.  In  order  to  ensure  relaxation  in 
accommodative  spasm  the  atropin  solution  (1  per  cent)  should 
be  used  four  times  a  day  for  several  days,  or  for  a  week  in  obsti- 
nate cases. 

The  diagnosis  of  the  cause  of  the  spasmodic  action  is  not 
always  easily  made.  If  the  spasm  is  not  due  to  refractive  error, 
which  is  by  far  the  most  common  cause,  hysteria,  cerebral  lesion, 
or  other  irritative  affection  may  be  suspected,  according  to  the 
attendant  circumstances. 

Treatment. — This  consists  in  removal  of  the  cause,  if 
possible.  Any  refractive  error  which  may  be  present  must  be 
corrected,  and  in  order  that  the  eyes  may  adapt  themselves  to  the 
glasses  it  may  be  necessary  to  continue  the  application  of  atropin 
for  several  weeks  or  longer. 

Paresis   and    Paralysis   of   Accommodation 

Weakness  of  accommodation  is  a  common  accompaniment 
of  the  general  physical  debility  following  severe  constitutional 
diseases  ;  but  in  addition  to  this  enfeeblement,  there  is  also  exerted 
by  certain  affections  a  direct  detrimental  action  upon  the  nerves 
of  accommodation. 

Diphtheritic  Paralysis. — This  may  consist  in  diminution 
(paresis),  or  in  complete  abolition  (paralysis)  of  the  accommo- 
dative function.  In  such  cases  the  diphtheritic  toxin  produces  a 
peripheral  ciliary  neuritis.  The  inflammation  also  frequently 
affects  other  branches  of  the  third  nerve,  causing  ptosis  and  diver- 
gent strabismus. 

Diphtheritic  paralysis  is  not  confined  to  the  third  nerve ;  the 
palatal  muscles  are  also  frequently  affected.  Paralytic  symptoms 
occur  after  subsidence  of  the  febrile  stage,  usually  in  the  second 
or  third  week  of  convalescence.  Complete  recovery  follows 
usually  in  about  a  month. 

Syphilitic  Paralysis. — This  results  from  injury  to  the 
nerves  or  their  centers  by  gummatous  deposit  or  degeneration. 
Accommodation  may  be  paralyzed  without  involvement  of  the  iris, 
or  there  may  be  both  cycloplegia  and  mydriasis  (internal  ophthal- 
moplegia), with  or  without  paralysis  of  the  external  ocular 
muscles. 

Paralysis  Caused  by  Non-syphilitic  Brain  Lesion. — 
Paresis  or  complete  paralysis  of  accommodation  may  also  result 


Presbyopia  and  Anomalies  of  Accommodation  265 

from  alcohol  or  tobacco  poisoning,  from  meningitis,  brain  tumor, 
or  other  cerebral  affection.  Here,  as  in  syphilitic  nuclear  disease, 
there  may  be  cycloplegia  with  or  without  mydriasis,  and  with  or 
without  involvement  of  the  extra-ocular  muscles. 

Glaucomatous  Paralysis. — The  abnormally  great  pres- 
sure upon  the  ciliary  nerves  in  glaucoma  produces  a  paralytic  state 
of  these  nerves,  with  a  consequent  deterioration  of  accommodative 
function. 

Accommodative  Paralysis  Arising  from  Other 
Diseases. — Various  diseases,  as  diabetes,  rheumatism,  gout, 
lithiasis,  and  also  severe  contusions  sometimes  exert  a  direct 
action  upon  the  accommodative  apparatus,  causing  an  abridg- 
ment or  abolition  of  function. 

Artificial  Cycloplegia. — We  have  already  learned  that 
the  instillation  into  the  conjunctival  sac,  or  the  internal  adminis- 
tration of  large  doses,  of  atropin  and  similar  drugs  produces 
paralysis  of  accommodation  and  mydriasis  (Chapter  X). 

Symptoms  and  Diagnosis  of  Accommodative  Paralysis. 

— The  most  characteristic  symptom  of  accommodative  paralysis 
is,  except  in  myopia,  the  inability  to  see  near  objects  clearly.  As 
macropsia  occurs  in  spasm  of  accommodation,  so  micropsia  is 
a  not  uncommon  manifestation  of  cycloplegia.  The  attendant 
mydriasis  may  give  rise  to  dazzling,  dizziness,  and  nausea. 

The  diagnosis  is  made  by  ascertaining  the  amplitude  of 
accommodation  and  excluding  presbyopia.  The  amplitude  may  be 
determined  with  Jaeger's  test  types  and,  if  the  pupil  is  moderately 
dilated,  by  skiascopy.  If,  after  the  static  refraction  has  been 
ascertained,  the  person  under  examination  is  directed  to  look  at 
an  object  placed  near  the  punctum  proximum  of  cenvergence, 
the  examiner  may  decide  in  accordance  with  the  principles  of 
skiascopy  whether  the  eye  becomes  myopic  through  exercise  of 
accommodation,  and,  if  so,  to  what  extent. 

Treatment  of  Accommodative  Paralysis. — The  treat- 
ment depends  upon  the  cause  of  the  paralysis,  which  must  be  de- 
termined, if  possible.  Hygienic  and  tonic  treatment  for  the  debili- 
tated, mercury  and  iodides  for  syphilis  are  evident  indications.  In 
chronic  non-syphilitic  brain  lesions  not  much  can  be  done.  If 
mydriasis  coexists,  and  especially  in  artificial  cycloplegia,  dazzling 
must  be  prevented  by  the  use  of  tinted  glasses. 


266  Errors  of  Refraction 

Loss  of  Accommodation  from  Absence  or  Luxation 
of  the  Lens. — Accommodation  is  clearly  impossible  when  the 
crystalline  lens  is  absent  from  the  eye,  for  the  most  energetic 
contraction  of  the  ciliary  muscle  does  not  increase  the  curvature 
of  the  cornea  to  a  degree  capable  of  measurement  with  the 
ophthalmometer.  The  apparent  accommodation  which  sometimes 
occurs  in  such  eyes  is  due  to  contraction  of  the  pupil  and  to- 
unusual  ability  to  interpret  diffusion-images. 

In  luxation  of  the  lens  the  condition  resembles  aphakia  if 
the  lens  does  not  lie  in  the  pupillary  space.     On  the  other  hand,    . 
in  partial  luxation,  the  refractive  power  of  the  eye  is  usually  in- 
creased. 

The  following  authorities  have  been  consulted  in  the  prepara- 
tion of  the  foregoing  chapter : 

Donders,  Anomalies  of  Refraction  and  Accommodation;  and 
Ueber  scheinbare  Accommodation  bei  Aphakie,  Arch,  fur 
Ophthal.,  1873. 

Aristotle,  Opera  (Didot's  Greek-Latin  Ed.),  Prob.,  sec.  xxxi. 

Landolt.  Refraction  and  Accommodation  of  the  Eye. 

Weeks,  Intra-Ocular  Muscles,  Posey  and  Spiller's  Eye  and 
Nervous  System. 

Jaeger,  Schrift  Scalcn. 

Oliver,  New  Series  of  Metric  Test  Letters  and  Words  for 
Determining  the  Amount  and  Range  of  Accommodation.  Tr.  Am. 
Ophth.  Soc,  1885,  and  Med.  News,  1886. 


PART    IV 

DISORDERS    OF    MOTILITY 


CHAPTER  XVI 

OPTOMETRY  OF  THE  MOTOR  APPARATUS 

Before  entering  upon  the  details  of  the  methods  of  deter- 
mining the  condition  of  the  muscular  apparatus  of  the  eyes  we 
must  become  familiar  with  the  various  terms  which  we  shall  have 
occasion  to  use  in  dealing  with  this  subject.  Some  of  :hese  have 
already  been  mentioned  in  Chapter  IX. 

We  are  indebted  to  Stevens  for  the  modern  nomenclature  of 
the  muscular  equilibrium  of  the  eyes.  He  uses  the  following 
classification : 

(i)      The  relation  of  the  visual  lines  to  each  other. 

(2)  The  relation  of  tJic  normal  visual  planes  to  the  cranium. 

(3)  The  relation  of  the  vertical  meridians  to  the  cranium. 

(4)  Spasmodic  affections  of  the  eye  muscles  from  func- 
tional causes. 

( 1 )  The  study  of  the  first  relation  will  occupy  the  greater 
part  of  our  attention.  As  regards  this  relation  orthophoria 
(6Pe6s,  right;  4>opa,  a  tending)  is  the  ideal  condition.  Ortho- 
phoria is  defined  as  a  tending  of  the  visual  lines  in  parallelism,  the 
determination  being  made  for  a  point  not  less  than  six  meters 
distant.  In  orthophoria  the  visual  line  of  each  eye  passes  through 
the  distant  point  of  fixation,  even  when  one  eye  is  excluded  from 
vision,  as  by  covering  it  with  a  card. 

Deviation  from  orthophoria  may  be  either  latent  or  manifest. 
A  latent  deviation  is  called  hctcrophoria;  a  manifest  deviation  is 
called  heterotropia. 

In  heterophoria  there  is  binocular  vision,  but  when  one  eye  is 
excluded  from  vision  its  visual  line  undergoes  a  deviation.  In 
accordance   with   the  direction  of  this  deviation     there     results 

267 


268  Disorders  of  Motility 

esophoria,  deviation  inward ;  exophoria,  deviation  outward ;  hyper- 
phoria, deviation  upward ;  and  hypophoria,  deviation  downward. 
Similarly  a  deviation  irtward  and  upward  constitutes  hyper- 
esophoria;  a  deviation  downward  and  outward  is  hypo-exophoria, 
etc. 

In  heterotopia  vision  is  monocular  and  one  eye  deviates  even 
when  uncovered.  In  accordance  with  the  direction  of  deviation 
heterotropia  is  subdivided  into  esotropia,  exotropia,  hypertropia, 
hypotropia  and  their  compounds. 

Heterotropia  is  also  called  squint  or  strabismus.  Esotropia  is 
internal  or  convergent  strabismus ;  exotropia  is  external  or  diver- 
gent strabismus;  hypertropia  is  strabismus  sursumvergens ;  and 
hypotropia  is  strasbismus  deorsumvergens.  The  latter  two  of 
these  terms,  being  less  simple  than  the  terms  of  the  newer 
nomenclature  of  Stevens,  are  gradually  falling  into  disuse,  but 
convergent  and  divergent  strabismus,  which  are  very  expressive, 
remain  in  favor. 

There  are  two  essentially  different  kinds  of  heterotropia : 
concomitant  or  comitant,  in  which  the  deviation  remains  the  same 
in  the  various  directions  of  the  gaze ;  and  paralytic,  in  which  the 
deviation  changes  as  the  direction  of  the  gaze  is  altered. 

Comitant  deviations  are  divided  into:  (a)  alternating,  when 
sometimes  one  eye  and  sometimes  the  other  deviates;  and  (b) 
monocular  when  the  deviation  is  always  confined  to  the  same  eye. 

Another  division  is :  intermittent  or  periodic;  and  constant  or 
continuous. 

(2)  As  regards  the  relation  of  the  visual  plane  to  the 
cranium,  there  are  five  possible  conditions. 

(a)  Euthophoria,  the  ideal  condition,  is  that  in  which  the 
passive  adjustment  of  the  visual  plane  coincides  with  the  plane 
of  the  horizon,  or  very  nearly  so. 

(b)  Anophoria  is  that  condition  in  which  the  passive  ad- 
justment of  the  visual  plane  is  decidedly  above  the  horizontal 
plane. 

(c)  Katophoria  is  that  condition  in  which  the  passive  ad- 
justment is  decidedly  below  the  visual  plane. 

(d)  Anotropia,  and  (e)  katotropia  bear  the  same  relation 
to  anophoria  and  katophoria  as  heterotropia  does  to  heterophoria ; 
that  is,  anotropia  and  katotropia  are  manifest  errors,  whereas 
anophoria  and  katophoria  are  tendencies,  not  deviations. 


Optometry  of  the  Motor  Apparatus' 


269 


(3)  As  regards  the  relation  of  the  vertical  meridians  to  the 
cranium,  the  ideal  condition  is  such  that  the  normal  vertical 
meridian  of  each  eye  remains  vertical  in  passive  adjustment.  Any 
deviation  from  this  condition  is  declination  (Stevens)  ;  or  cyclo- 
phoria,  or  cyclotropia  (Savage). 

(4)  Under  the  head  of  spasmodic  affections  we  consider 
nystagmus. 

0 


FIG.    IIO 
Showing  the  position  on  the  retina  of  the  false  image   (7)   in  strabismus. 


Diplopia. — We  know  that  distinct  vision  is  possible  only 
when  the  image  falls  upon  the  fovea,  and  that  the  normal  fusion 
into  a  single  perception  of  the  two  visual  impressions  is  possible 
only  when  the  image  falls  upon  the  fovea  of  each  eye.  When  the 
two  visual  lines  do  not  meet  at  the  object  of  vision  one  eye  (the 
fixing  eye)  will  be  so  directed  as  to  receive  the  image  upon  its 
fovea,  while  the  other  eye  receives  the  image  upon  an  eccentric  part 
of  its  retina,  and  at  the  same  time  some  other  external  object  casts 
its  image  upon  the  fovea  of  this  eye.  Under  experimental  condi- 
tions we  can  see  the  two  objects  whose  images  are  formed  on  the 


270 


Disorders  of  Motility 


two  foveas,  as  when  a  part  of  a  familiar  picture  is  made  with  a 
stereoscope  to  fall  upon  the  fovea  of  one  eye  and  the  complement 
of  this  picture  is  made  to  fall  upon  the  fovea  of  the  other  eye. 
Thus,  the  image  of  a  horse  being  presented  to  one  eye  a-nd  that  of 
a  man  in  the  attitude  of  rider  to  the  other  eye,  we  form  the  mental 
picture  of  the  rider  upon  the  horse.     But  in  ordinary  vision  the 


FIG.    Ill 
Projection    (I  O)    of  the   false  image. 


image  which  falls  upon  the  fovea  of  the  deviating  eye  will  be 
disregarded,  while  the  eccentrically  placed  image  of  the  object 
which  the  other  eye  is  fixing  will  be  manifested  to  consciousness 
as  the  second  image  of  the  object  of  fixation.  This  is  binocular 
diplopia.  Two  images  of  the  object  of  vision  are  seen:  one,  the 
true  image,  is  formed  upon  the  macula  of  the  fixing  eye;  the 
other,  the  false  image,  which  is  less  distinct,  is  formed  on  a  part 
of  the  retina  of  the  deviating  eye  more  or  less  removed  from 
the  macula. 


Optometry  of  the  Motor  Apparatus  271 

Orientation  of  the  False  Image. — In  convergent  strabis- 
mus the  deviating-  eye  receives  the  image  of  the  object  of 
fixation  upon  a  part  of  the  retina  which  is  situated  on  the  nasal 
side  of  the  fovea  (Fig.  no).  In  normal  vision  this  part  of  the 
retina  could  be  stimulated  only  by  an  object  situated  on  the  tem- 
poral side  of  the  object  of  fixation  (Fig.  in).  The  subject  of 
strabismus  therefore  not  being  able  to  readjust  the  nerve  associa- 
tions, assigns  such  position  to  the  object  of  vision  as  an  object 
stimulating  the  same  part  of  the  retina  would  have  if  perceived 
through  an  eye  in  its  normal  position. 

In  convergent  strabismus,  the  nasal  side  of  the  retina  being 
stimulated  in  the  deviating  eye,  the  false  image  is  displaced  to  the 
temporal  side ;  that  is,  to  the  right  side  if  the  right  eye  deviates 
inward,  and  to  the  left  side  if  the  left  eye  deviates  inward.  The 
true  image  being  seen  in  its  correct  position,  the  false  image 
appears  (relatively  to  the  true  image)  to  lie  on  the  side  corre- 
sponding to  the  deviating  eye.  This  is  called  homonymous  dip- 
lopia. 

In  divergent  strabismus  the  opposite  condition  occurs.  The 
false  image  lies  on  the  temporal  side  of  the  retina  and  it  is  pro- 
jected towards  the  nasal  side.  It  thus  appears  to  be  on  the  side 
opposite  to  the  deviating  eye.    This  is  crossed  diplopia. 

Similarly,  in  hypertropia  the  false  image  of  the  higher  eye 
appears  to  be  lower  than  the  true  image  of  the  fixing  eye. 

The  displacement  of  the  false  image  is  always  in  the  direction 
opposite  to  that  of  the  false  position  of  the  eye.  When  the  eye 
turns  up  the  false  image  is  accordingly  lower  than  the  true  image 
of  the  other  eye,  and  when  the  eye  turns  down  the  false  image  is 
higher  than  the  true  image.  So  also  when  there  is  extorsion  of 
the  vertical  meridian  of  the  eye  there  is  intorsion  of  the  corre- 
sponding image  and  vice  versa. 

Primary  and  Secondary  Deviation. — When  one  eye  is  used 
for  fixation  while  the  other  squints,  the  angular  deviation  of  the 
squinting  eye  constitutes  the  primary  deviation.  When  the  fixing 
eye  is  covered  and  the  squinting  eye  moves  into  the  fixation 
position  while  the  other  eye  now  deviates  the  resulting  deviation 
of  the  good  eye  constitutes  the  secondary  deviation. 

Breadth  of  Fusion. — Since  a  prism  interposed  between  an 
eye  and  the  point  of  fixation  changes  the  path  of  the  light  which 
enters  the  eye  from  this  point,  it  is  apparent  that  if  in  binocular 


2.J2.  Disorders  of  Motility 

fixation  we  place  a  prism  before  one  eye  the  light  which  enters 
the  eye  through  the  prism  does  not  fall  upon  the  macula  of  this 
eye  and  in  consequence  of  this  diplopia  results.  But  so  great  is 
the  natural  desire  to  avoid  diplopia  and  to  secure  binocular  vision 
that  as  far  as  the  eye  is  able  to  do  so,  it  quickly  readjusts  its 
position  and  assumes  that  direction  which  causes  the  image  to  fall 
upon  the  macula.  The  strongest  prism  which  can  thus  be  over- 
come for  the  accomplishment  of  binocular  vision  measures  the 
breadth  of  fusion. 

The  fusion  potver  varies  greatly  in  different  directions.  It 
is  greatest  in  convergence.  We  can,  by  the  interposition  of  prisms 
see  a  distant  point  of  light  singly  while  the  eyes  behind  the  prisms 
are  exercising  a  convergence  of  7  ma  or  even  more.  This  amount 
of  convergence  is  necessary  to  overcome  the  action  of  a  prism  of 
about  25  A  before  each  eye.  It  is  apparent  that  the  bases  of  the 
prisms  must  be  placed  out,  towards  the  temples,  in  order  that  the 
point  of  fixation  may  be  displaced  nasalward,  as  is  required  for 
binocular  fixation  of  a  distant  point  with  the  eyes  in  convergence. 
Prisms  having  their  bases  towards  the  temples  are  therefore  called 
converging  prisms. 

Similarly,  it  is  apparent  that  prisms  with  their  bases  in, 
towards  the  nose,  diminish  convergence  or  cause  an  actual 
divergence  of  the  visual  lines.  Such  prisms  are  called  diverging 
prisms.  The  normal  breadth  of  fusion  in  divergence  is  about  1 
ma,  as  represented  by  a  prism  of  y/2  A  before  each  eye. 

In  the  vertical  meridian  the  breadth  of  fusion  is  less.  Only 
a  very  weak  prism  (about  3 A  base  up  or  down)  can  be  interposed 
between  the  eye  and  the  fixation  point  without  producing  diplopia. 

There  still  remains  to  be  mentioned  the  power  of  rotating  the 
retinal  meridians  for  the  avoidance  of  diplopia.  This  question  has 
been  studied  chiefly  by  Stevens  and  by  Savage.  Both  authors 
agree  that  the  breadth  of  fusion  for  a  vertical  line  is  considerably 
greater  than  that  for  a  horizontal  line.  According  to  Stevens, 
the  amplitude  of  rotation  without  diplopia  is,  for  a  vertical  line, 
about  io°  in  or  out,  or  slightly  more  out.  For  a  horizontal  line 
he  assigns  30  up  or  dozvn  as  the  normal  amplitude. 

Artificial  Diplopia. — When  the  strength  of  the  prism  which 
is  interposed  between  the  eye  and  the  point  of  fixation  is  greater 
than  the  amplitude  of  fusion,  insuperable  diplopia  results.  We 
make  use  of  this  phenomenon,  that  is,  we  create  an  artificial  diplo- 


Optometry  of  the  Motor  Apparatus  273 

pia,  in  most  of  our  methods  of  determining  the  muscular  equilib- 
rium of  the  eyes.  When  the  diplopia  can  no  longer  be  overcome 
the  non-fixing  eye  presumably  assumes  its  position  of  equilibrium 
as  determined  by  the  muscular  adjustments  under  a  minimum  of 
innervation. 

Tests  Used  in  Motor  Optometry 

Of  the  various  methods  available  in  this  branch  of  optometry 
some  are  subjective,  others  are  objective.  The  two  groups  of 
tests  are,  however,  more  closely  associated  than  the  corresponding 
groups  in  refractive  optometry,  in  which  we  learned  to  employ 
first  one  group  and  then  the  other.  In  motor  optometry  we  do 
not  make  this  distinction.  We  proceed  in  a  routine  manner,  using 
subjective  and  objective  tests  in  any  order  which  may  be  conven- 
ient. For  instance,  it  is  a  logical  procedure  to  measure  first  the 
converging  power  and  next  the  diverging  power  of  the  muscles. 
The  former  measurement  may  be  made  objectively,  while  the 
latter  must  be  made  by  means  of  a  subjective  method. 

Cover  Test. — The  simplest  method  of  testing  the  muscular 
equilibrium  consists  in  covering  one  eye,  while  the  other  eye  is 
directed  towards  some  point  of  fixation,  and  watching  the  be- 
havior of  the  eye  at  the  moment  of  its  uncovering. 

In  making  use  of  this  method  for  determining  the  muscular 
equilibrium  we  direct  the  person  undergoing  examination  to  look 
at  a  distant  point  of  light.  If,  while  he  performs  fixation  with  one 
eye,  the  other  eye,  at  the  moment  of  uncovering,  makes  a  move- 
ment of  redress  in  order  that  it  also  may  perform  fixation,  we 
know  that  binocular  vision  exists,  and  that  there  is  a  deviation 
from  orthophoria.  If  the  movement  is  inward,  the  eye  has  devi- 
ated outward  under  cover,  and  there  is  a  condition  of  exophoria. 
If,  on  the  other  hand,  the  eye  moves  outward  on  being  uncovered, 
there  is  esophoria.  If  it  moves  downward,  there  is  hyperphoria. 
If  it  moves  upward  there  is  hypophoria,  that  is,  there  is  hyper- 
phoria of  the  other  eye. 

If,  when  the  eye  is  uncovered  there  is  no  movement  of 
redress,  there  is  orthophoria,  or  else  the  eye  does  not  perform 
fixation,  vision  being  monocular  and  accomplished  with  the  other 
eye. 

When  vision  is  monocular  the  muscular  error  is  manifested 
as  strabismus,  which,  as  a  rule,  the  examiner  may  detect  by  visual 


274  Disorders  of  Motility 

inspection.  We  then  use  the  cover  test  to  ascertain  whether  the 
strabismic  eye  is  capable  of  fixation.  For  this  purpose  we  cover 
the  fixing  eye,  and  note  whether  the  other  eye  moves  into  the  fixa- 
tion position. 

We  may  approximately  estimate  the  degree  of  imbalance  by 
observing  the  strength  of  the  prism  which  is  required  to  annul  the 
movement  of  redress,  but  as  it  is  difficult  to  observe  a  very  slight 
movement  of  the  eye,  other  tests  are  more  convenient  for  this 
purpose. 

Duane's  Parallax  Test. — This  test  is  another  method  of 
applying  the  cover  test ;  but  instead  of  using  it  as  an  objective  test 
and  observing  the  movement  of  redress,  we  request  the  examinee 
to  say  whether,  as  a  card  is  passed  quickly  from  one  eye  to  the 
other,  there  is  an  apparent  movement  of  the  distant  point  of  light. 
If  the  light  appears  to  move  to  the  right  when  the  right  eye  is  un- 
covered, there  is  homonymous  diplopia  (inward  deviation)  ;  if  it 
moves  to  the  left  when  the  right  eye  is  uncovered  there  is  crossed 
diplopia  (outward  deviation),  and  so  on.  The  prism  which 
annuls  the  apparent  movement  corrects  the  deviation.  In  prac- 
tice it  is  better  to  increase  the  strength  of  the  prism  until  a  slight 
movement  commences  in  the  opposite  direction.  The  prism  which 
has  this  effect  is  about  2A  stronger  than  the  prism  which  corrects 
the  deviation.     (Dnane.) 

Colored  Glass  Test. — When  a  colored  glass  is  placed  before 
one  eye  the  impulse  for  binocular  vision  is  materially  reduced, 
and  in  marked  heterophoria  two  images  of  a  flame,  one  of  them 
•colored  by  the  glass  and  the  other  the  natural  color  of  the  flame, 
\will  be  seen.  In  applying  this  test  we  generally  use  the  red  or 
the  cobalt  blue  glass  of  the  trial  case,  and  have  the  examinee  look 
at  a  candle  flame  or  other  small  light  at  a  distance  of  five  or  six 
meters.  We  then  determine  the  kind  of  heterophoria  present 
from  the  relative  position  of  the  double  images. 

This  method  is  very  convenient  in  demonstrating  the  co- 
existence of  lateral  and  vertical  imbalance,  such  as  hyper-esophoria 
and  hyper-cxophoria,  but  it  is  not  very  accurate  for  the  measure- 
ment of  the  amount  of  heterophoria,  for  if  we  attempt  to  measure 
the  displacement  of  the  false  image  by  the  prism  which  super- 
poses it  upon  the  true  image,  we  find  that  when  the  two  images 
are  brought  near  together  they  are  fused  by  the  impulse  for 
"binocular  vision. 


Optometry  of  the  Motor  Apparatus  275 

Graefe's  Test. — Graefe's  test  consists  in  the  production  of 
insuperable  diplopia  by  means  of  a  prism.  Since  under  this  condi- 
tion binocular  vision  is  impossible,  the  subject  of  examination 
makes  no  effort,  or,  at  the  most,  a  very  slight  effort,  to  adjust 
the  muscular  apparatus  for  single  vision. 

To  test  the  lateral  equilibrium  we  place  a  prism  of  8  A  or 
10 A,  with  its  base  down,  before  one  eye  of  the  examinee,  while 
he  looks  at  a  point  of  light  at  a  distance  or  five  or  six  meters. 
Because  of  the  diplopia  created  by  the  prism  two  images  of  the 
light  will  be  seen.  Since  the  base  of  the  prism  is  down,  the  false 
image  will  be  the  higher;  and  if  there  is  orthophoria  as  regards 
the  lateral  equilibrium  the  two  images  will  be  in  the  same  vertical 


FIG.    112 


line.  If  there  is  esophoria  the  false  image  will  lie  on  the  side 
corresponding  to  the  eye  which  has  the  prism  before  it  (homony- 
mous diplopia )  ;  if.  on  the  other  hand,  there  is  exophoria  the  false 
image  will  lie  on  the  opposite  side  (crossed  diplopia).  The  prism 
which  annuls  the  lateral  displacement  measures  the  heterophoria. 

Maddox  recommends,  as  easier  of  accurate  application,  the 
double  prism  (Fig.  112).  This  is  placed  before  one  eye  so  that 
the  double  base  line  bisects  the  pupil.  Two  images  are  then  seen 
with  this  eye.  In  testing  the  lateral  muscles  the  base  of  the  prism 
is  horizontal,  and  one  image  is  vertically  over  the  other.  In  ortho- 
phoria the  single  image  seen  with  the  other  eye  lies  between  the 
double  images  and  in  the  same  vertical  line  with  them.  In  lateral 
heterophoria  the  middle  image  is  not  in  the  same  vertical  line  with 
the  other  two  images,  and  the  prism  which  brings  all  three  images 
into  the  same  vertical  line  measures  the  heterophoria. 

In  measuring  the  vertically  acting  muscles  the  base  of  the 
prism  is  vertical,  and  the  three  images  lie  in  the  same  horizontal 
line  in  orthophoria.     In  hyperphoria  the  middle  image  is  not  in 


276 


Disorders  of  Motility 


the  same  horizontal  line  with  the  other  two  images,  and  the  prism 
which  brings  all  three  images  into  the  same  horizontal  line  meas- 
ures the  hyperphoria. 

In  applying  this  test  for  finding  the  vertical  equilibrium  we 
place  a  prism  of  10A  with  its  base  in  before  one  eye,  and,  as 


fig.  113 

Prism  Bar. 


before,  have  the  patient  look  at  a  distant  point  of  light.  If  there 
is  no  heterophoria  in  the  vertical  direction  the  two  images  will  lie 
in  the  same  horizontal  plane ;  but  if  one  eye  tends  to  a  higher  plane 
than  the  other  eye,  the  image  which  corresponds  to  the  higher 
eye  will  be  the  lower,  and  vice  versa.     We  measure  the  degree 


fig.  114 

Rotary  Prism. 

of  hyperphoria  by  the  prism  which  places  the  two  images  in  the 
same  horizontal  plane. 

In  the  application  of  Graefe's  test  we  may  select  the  proper 
prism  from  the  trial  case;  or  we  may  use  a  prism  bar  (Fig.  113) 
or  a  rotary  prism  (Fig.  114),  but  the  most  convenient  apparatus 
is  the  phorometer  of  Stevens  (Fig.  115).    This  consists  of  a  pair 


Optometry  of  the  Motor  Apparatus 


277 


of  prisms,  each  of  5  A,  suitably  mounted  upon  a  bracket  or  stand, 
and  so  arranged  that  by  rotating  one  prism  a  corresponding 
motion  is  conveyed  to  the  other.  By  this  means,  when  the  base 
of  one  prism  is  directly  up  (towards  the  brow)  the  base  of  the 
other  is  directly  down;  when  the  base  apex  line  of  one  prism  is 
horizontal  that  of  the  other  is  likewise  horizontal,  both  bases  being 
in  (towards  the  nose)  or  both  being  out  (towards  the  temples). 
In  testing  the  lateral  muscles  vertical  diplopia  is  produced  by  plac- 
ing the  base  of  one  prism  up  and  that  of  the  other  prism  down.  If 


fig.  115 

Stevens    Phorometer 

the  double  images  do  not  appear  in  a  vertical  line,  there  is  esopho- 
ria  or  exophoria.  By  rotating  the  prism  the  images  are  shifted 
so  that  one  of  them  lies  directly  over  the  other,  the  degree  of  im- 
balance being  indicated  on  a  scale  in  accordance  with  the  amount 
of  rotation  required.  In  testing  the  vertically  acting  muscles  the 
prisms  are  rotated  into  the  horizontal  plane  for  the  production  of 
lateral  diplopia,  when  any  existing  hyperphoria  will  be  manifested 
by  one  of  the  double  images  being  higher  than  the  other.  The 
degree  of  imbalance  can  be  ascertained  by  rotation  of  the  prisms 
until  the  two  images  lie  in  the  same  horizontal  plane. 

Maddox  Rod  Test. — The  Maddox  rod  consists  of  a  small 
glass  cylinder,  or  a  series  of  parallel  cylinders  (Fig.  116),  mounted 


278 


Disorders  of  Motility 


in  an  opaque  diaphragm  of  suitable  size  to  be  placed  in  a  trial 
frame.  The  cylinder  produces  very  great  magnification  of  images 
in  the  direction  at  right  angles  to  its  axis,  so  that  a  small  flame  as 
seen  through  this  cylinder  appears  as  a  long  streak  of  light. 
Hence,  if  the  cylinder  is  placed,  with  its  axis  horizontal,  before 


FIG.    Il6 
Maddox  Rod. 

one  eye  while  a  small  light  is  viewed  binocularly,  the  vertical 
streak,  as  seen  with  one  eye,  cannot  be  fused  with  the  flame  as 
seen  with  the  other  eye,  and  in  the  abandonment  of  the  attempt 
to  effect  fusion  the  eyes  assume  their  position  of  equilibrium.  If 
the  streak  of  light  appears  to  pass  vertically  through  the  flame, 


fig.  117 

ROD    TEST, 
(o)   Orthophoria;     (b)   esophoria;     (f)   exophoria.    the    rod   being   before   the    right   eye. 

there  is  no  disorder  of  lateral  equilibrium;  if  the  streak  is  dis- 
placed homonymously,  there  is  esophoria,  and  if  there  is  crossed 
displacement  the  condition  is  that  of  exophoria  (Fig.  117).     The 


Optometry  of  the  Motor  Apparatus 


279 


prism  which  causes  the  streak  to  pass  vertically  through  the  flame 
measures  the  lateral  heterophoria. 

If  we  place  the  rod  vertically  the  streak  of  light  appears  in 
the  horizontal  direction.  If  there  is  no  vertical  heterophoria  the 
streak  passes  through  the  middle  of  the  light.  If  there  is  hyper- 
phoria of  the  eye  before  which  the  rod  is  placed  the  streak  is 
below  the  light,  and  if  there  is  hypophoria  of  this  eye  (hyper- 
phoria of  the  other  eye)  the  streak  is  above  the  light.  The  prism 
which  causes  the  streak  to  pass  horizontally  through  the  light 
measures  the  hyperphoria. 

Stenopaeic  Lens  Test  (Stevens). — A  strong  convex  lens 
(13  D)  is  covered  by  an  opaque  disk  having  a  small,  circular 
opening  at  its  center  (Fig.  118).  If  one  looks  through  this 
aperture,  a  distant  flame  appears  as  a  circular  blur  of  light  (Fig. 
119).     If  the  muscles  are  normally  balanced,  the  flame,  as  seen 


JO 


FIG.    119 
Orthophoria 


FIG.    Il8 
Stenopaeic    Lens 


^cii,. 


FIG.    120 

Heterophoria 


by  the  fellow-eye  (which  is  uncovered),  will  appear  to  be  at  the 
center  of  the  blurred  image.  In  heterophoria  the  clear  image  will 
not  lie  at  the  center  of  the  field,  but  will  be  displaced  in  accord- 
ance with  the  kind  and  degree  of  muscular  error,  which  is  meas- 
ured by  the  prism  required  to  bring  the  image  of  the  flame  into 
the  center  of  the  field. 

Measurement  of  Convergence  and  Divergence. — A 
ready  method  of  measuring  the  converging  power  consists  in 
having  the  examinee  look  at  the  point  of  a  pencil,  which  we  hold 
in  the  median  plane,  while  we  gradually  move  the  pencil  nearer 
to  his  eyes  until  we  see  one  eye  abandon  the  effort  to  maintain 
fixation  and  turn  outward.     The  position  of  the  pencil  when,  this 


28o 


Disorders  of  Motility 


occurs  marks  the  near  point  of  convergence.  If  the  amplitude 
is  normal,  convergence  can  be  maintained  until  the  pencil  is  about 
four  inches  (10  cm)  from  the  eyes. 

If  we  wish  to  make  an  accurate  measurement  in  meter  angles 
we  use  the  ophthalmo-dynamometer  of  Landolt  (Fig.  121). 


FIG.   121 
Ophthalmodynamometer. 

We  measure  the  diverging  pozver  by  means  of  prisms.  If 
we  place  a  prism  with  its  base  in  before  one  eye,  light  from  a 
distant  point  can  fall  upon  both  foveas  only  when  the  visual  lines 
are  divergent.  Therefore,  the  strongest  prism  with  which  binoc- 
ular vision  can  be  maintained  measures  the  diverging  power.  The 
average  normal  diverging  power  is  represented  by  a  prism  of  7  A 
(base  in)  before  one  eye;  or  by  a  prism  of  3^2 A  before  each 
eye.  This  corresponds  to  1  ma  of  divergence,  as  reckoned  upon 
an  interocular  base  line  of  64  mm. 

Measurement  of  Prism  Convergence. — Prism  conver- 
gence has  already  been  described  as  the  breadth  of  fusion  in  con- 
vergence. We  have  learned  that  this  may  reach  7  ma.  Such  an 
amount,  however,  is  not  usually  manifested  at  the  first  examina- 
tion. But  the  increase  of  the  fusion  power  which  results  from 
training  does  not  signify  that  the  muscles  have  been  strengthened 
by  practice.     It  means  only  that  the  person  has  learned  to  con- 


Optometry  of  the  Motor  Apparatus  281 

verge  for  a  distant  object  just  as  if  the  object  were  very  near 
the  eyes. 

The  term  adduction  was  improperly  applied  by  von  Graefe 
to  express  prism  convergence,  and  abduction  was  with  equal  im- 
propriety used  to  express  divergence.  These  misnomers  remain 
in  common  use.  In  accordance  with  the  definitions  already  given 
adduction  refers  to  any  rotation  of  the  eye  inward,  and  abduction 
to  any  rotation  outward,  as  in  the  movement  of  both  eyes  to  the 
right  or  to  the  left. 

Measurement  of  Strabismus 

The  following  tests  are  used  in  the  measurement  of  hetero- 
tropia  or  strabismus. 

Graefe's  Linear  Method. — This .  method  is  suitable  only 
for  horizontal  deviations,  which  we  can  measure  approximately  in 
the  following  way  if  the  squinting  eye  is  capable  of  fixation.  The 
patient  is  directed  to  look  at  a  distant  object  with  the  better  eye 
while  the  point  where  the  vertical  line  passing  through  the  border 
of  the  cornea  cuts  the  lower  lid  is  marked  in  ink.  The  better  eye 
is  then  covered  and  the  deviating  eye  moves  into  position  for 
fixation.  The  point  where  the  corresponding  vertical  line  cuts 
the  lower  lid  is  again  marked,  and  the  distance  between  the  points 
measures  the  strabismus   (Fig.  122).     In  an  eye  of  normal  size 


FIG.    122 
Linear   Measurement  of  the   Lateral   Excursions   of  the   Eye    (Alfred  Graefe). 

each  millimeter  of  displacement  corresponds  to  an  angle  of  devia- 
tion of  about  five  degrees. 

This  test  has  been  criticised  because  the  measurements  are 
made  from  the  linear  displacement  of  the  cornea  and  not  from  the 
actual  rotation  in  degrees  of  the  eye.  We  should  remember,  how- 
ever, that  the  principle  of  this  method  is  the  same  as  that  of  the 
tropometer,  which  is  usually  regarded  as  furnishing  one  of  the 
most  accurate  methods  available  for  measuring  ocular  rotations. 


282  Disorders  of  Motility 

Graefe's  method  is  therefore  a  rational  and  useful  test  for  the 
ready  and  approximate  measurement  of  strabismus.  The 
advantage  of  the  tropometer  is  that  it  enables  us  to  make  the 
observations  much  more  accurately  and  that  it  is  applicable  for 
measurements   in   other   directions  besides   the   horizontal   plane. 


fig.  123  fig.  124 

Javal's   Method.       Charpentier's   Method. 

When  the  squinting  eye  is  not  capable  of  fixation  we  can 
make  a  rough  guess  as  to  the  deviation  by  comparing  the  hori- 
zontal distance  of  the  pupillary  center  from  the  inner  canthus  with 
the  corresponding  distance  in  the  fixing  eye. 

The  Perimeter  Method. — \n  measuring  the  strabismus 
with  the  perimeter  by  Javal's  method  the  squinting  eye  is  placed 
at  the  center  of  the  arc.  while  the  fixing  eye  is  directed  to  a  distant 
point,  as  a  candle  light  five  or  six  meters  away  (Fig.  123).  A 
distant  fixation  point  is  taken  in  order  that  the  effect  of  converging 
for  a  near  point  may  be  avoided.  While  the  patient  looks  at  the 
light  the  examiner  moves  another  small  candle  flame  (or  an  electric 
light)  along  the  arc  of  the  perimeter  until  he.  being  directly  behind 
the  flame,  sees  the  corneal  image  in  the  middle  of  the  pupil  of  the 
squinting  eye.  The  error  which  is  due  to  the  fact  that  the  visual 
line  does  not  usually  pass  through  the  center  of  the  pupil  is  not 
sufficient  to  require  correction.  This  method  is  accurate,  but  when 
the  strabismus  is  slight  it  is  difficult  or  impossible  for  the  examiner 


Optometry  of  the  Motor  Apparatus  283 

to  place  his  head  in  the  proper  position  without  cutting  off  the 
patient's  view  of  the  fixation  light. 

This  difficulty  is  avoided  in  Charpentier's  method,  which, 
however,  is  otherwise  inferior  to  Javal's  method.  Charpentier's 
method  is  illustrated  in  Fig.  124.  As  in  Javal's  method,  the 
patient  looks  at  a  distant  candle  light,  but  in  this  method  the 
second  candle  flame  is  placed  at  the  fixation  spot  of  the  perimetric 
arc,  while  the  examiner  moves  his  eye  along  the  arc  until  he  sees 
the  reflected  image  of  the  candle  flame  in  the  middle  of  the  pupil 
of  the  squinting  eye.  We  see  from  the  diagram  that  the  angle 
which  his  position  marks  on  the  perimetric  arc  is  twice  the  angle 
of  deviation. 

Priestly  Smith's  Tape  Method. — Instead  of  measuring  the 
deviation  on  the  arc  of  a  perimeter  we  may  use  a  tangent  scale, 
the  markings  of  which  correspond  to  degrees  of  rotation  at  the 
specified  center.  ///  Priestly  Smitli's  method  (Fig.  125)  two 
pieces  of  tape  are  used.  The  first  of  these  is  one  meter  long,  and 
it  is  stretched  between  the  patient  and  the  examiner  for  the  purpose 
of  maintaining  the  proper  distance  between  them.     The  second 


fig.  125 

Priestly  Smith's  Tape  Method. 

tape  is  graduated  in  tangents  of  degrees  on  a  one  meter  radius. 
The  two  pieces  of  tape  are  attached  to  a  ring  placed  on  a  finger 
of  the  examiner's  hand — the  hand  in  which  he  holds  the  ophthal- 
moscope for  obtaining  the  corneal  reflections.  He  then  takes  the 
free  end  of  the  graduated  tape  lightly  between  two  fingers  of  the 


284 


Disorders  of  Motility 


other  hand,  at  which  the  patient  is  directed  to  look.  He  moves 
this  hand  until  he  sees  the  image  in  the  center  of  the  pupil  of  the 
squinting  eye,  when  he  reads  from  the  tape  the  number  of  degrees 
of  deviation.  This  is  a  simple  and  easy  method,  but  it  assumes 
that  the  rotation  of  the  squinting  eye  is  the  same  as  that  of  the 
fixing  eye.     This  is  not  true  in  paralytic  strabismus. 


PATIENTS  EYE 


SURCEONSEYE 


STRINC  | 
ONE  ME  THE 
LONC 


FIG.     126 

Tangent  Strabismometery   (Maddox). 

Maddox  Tangent  Scale. — Maddox 's  method  is  based  upon 
that  of  Priestley  Smith.  It  is  a  more  convenient  way  of  applying 
the  tangent  scale  principle.  The  patient  is  placed  facing  a  candle 
flame  at  the  meter-distance,  while  the  examiner  places  his  head 
between  the  patient  and  the  candle,  but  at  a  lower  level  so  as  not 
to  cut  off  the  latter's  view  of  the  candle  (Fig.  126).    The  patient 


FIG.    127 
Tangent    Scale    (Maddox). 

is  then  directed  to  look  at  successive  figures  on  the  scale  until  the 
corneal  reflex  appears  in  the  center  of  the  pupil  of  the  squinting 
eye.  The  degree  of  deviation  is  marked  by  the  number  at  which 
the  patient  must  look  in  order  that  the  desired  appearance  may 
be  obtained.    The  tangent  scale  is  shown  in  Fig.  127. 


Optometry  of  the  Motor  Apparatus 


285 


Worth's  deviometer  consists  of  a  Maddox  tangent  scale 
arranged  in  a  way  suitable  for  examining  young  children.  It 
carries  a  movable  electric  lamp,  which  can  be  quickly  lighted  and 
extinguished  so  as  to  attract  the  attention  of  the  child  to  any  part 
of  the  scale  at  the  will  of  the  operator. 

Measurement  of  the  Field  of  Fixation. — To  these 
various  tests  for  measuring  strabismus  we  must  add  the  measure- 
ment of  the  field  of  fixation,  which  is  of  very  great  importance, 
especially  in  paralytic  affections. 


fig.  128 

Stevens     Tropometer 


We  may  roughly  measure  this  field  by  carrying  a  pencil  about 
in  the  various  directions  of  the  gaze  while  the  patient  follows  its 
movements.  In  case  of  marked  limitation  of  movement  we  can 
easily  see  that  the  affected  eye  does  not  follow  its  fellow  as  it 
does  under  normal  conditions.  But  for  the  exact  determination 
of  the  ocular  rotations  we  use  either  the  perimeter  (or  the  tangent 
scale)  or  the  tropometer. 

The  chief  advantage  of  the  tropometer  is  that  it  eliminates  the 
necessity  of  the  examiner's  placing  his  head  in  inconvenient  posi- 
tions, as  is  required  in  objective  measurements  with  the  peri- 
meter, and  that  the  projection  of  the  nose  does  not  interfere  with 


286 


Disorders  of  Motility 


the  measurement  of  extreme  inward  rotation,  as  it  does  in  the 
use  of  the  perimeter. 

In  using  the  perimeter  for  measuring  the  field  of  fixation  we 
place  the  eye  to  be  examined  at  the  center  of  the  arc  and  note  the 
greatest  rotation  possible.    We  may  do  this  in  either  of  two  ways. 


fig.  129 

Worth-Black   Amblyoscope 


In  the  first  or  subjective  method  the  test  object  consists  of  small 
reading  matter  which  cannot  be  seen  in  indirect  vision.  The 
farthest  point  on  the  arc  to  which  this  can  be  removed  while  it  can 
be  distinguished  marks  the  rotatory  power  in  the  specified  direc- 
tion. In  the  second  or  objective  method  we  use  a  candle  or  other 
light  and  note  the  greatest  degree  of  rotation  which  can  be  made 
while  we  see  the  corneal  reflex  in  the  fixation  position. 

The  tropometer  of  Stevens  (  Fig.  128)  consists  of  a  telescope 
arranged  with  a  reflector  so  that  the  tube  of  the  telescope  is  at 
right  angles  to  the  examinee's  line  of  vision.  There  is  also  a  head 
rest  to  prevent  motion  of  the  head.  The  measurements  are  made 
by  means  of  a  scale  in  the  eye  piece,  in  the  construction  of  which 
it  is  assumed  that  the  position  of  the  center  of  rotation  does  not 
differ  much  from  that  of  the  normal  eye. 

In  using  the  tropometer  we  first  adjust  the  scale  while  the 


Optometry  of  the  Motor  Apparatus 


287 


examinee  looks  into  the  center  of  the  instrument;  we  then  note 
the  degree  marking  on  the  scale  when  he  turns  his  eye  as  far  as 
possible  in  the  direction  under  consideration. * 

Tests  of  Binocular  Vision. — We  may  under  ordinary  cir- 
cumstances assume  that  vision  is  binocular  when  our  tests  reveal 
binocular  fixation.  But  when  one  eye  is  much  inferior  to  the 
other  in  visual  acuity,  the  inferior  eye  may  perform  fixation  and 
enter  subordinately  into  the  visual  process  without  the  accomplish- 
ment of  true  stereoscopic  vision.  Again,  in  certain  cases  of  long- 
standing strabismus  in  which  central  fixation  is  not  possible  with 
the  squinting  eye,  the  false  image  in  this  eye  is  apparently  blended 
with  the  true  image  of  the  other  eye.  But  in  this  case  also  stere- 
oscopic vision  does  not  exist.  We  must  therefore  in  all  cases  of 
strabismus  take  means  to  ascertain  whether  stereoscopic  vision 
exists,  for  if  it  does  not,  we  should,  except  in  evidently  hopeless 
cases,  endeavor  to  institute  the  performance  of  this  function. 

Hering's  test  with  falling  bodies  is  well  known,  but  the  one 
test  upon  which  we  now  rely  is  that  with  the  stereoscope.  Worth's 


^ 


FIG.    130 
Test   Pictures  used   with   the   Amblyoscope 


amblyoscope,  with  the  improved  mechanical  adjustments  which 
have  been  added  by  Black  (Fig.  129),  furnishes  the  most  con- 
venient form  of  stereoscope  for  ascertaining  whether  or  not  binoc- 


*This  scale  has  been  incorrectly  described  by  some  writers  as  a  tangent  scale. 
Such  a  scale  would  give  erroneous  results,  for  it  is  the  chord  of  the  arc  of  rotation, 
not  the  tangent,  which  we  measure.  The  scale,  as  constructed  in  the  Stevens  tropo- 
meter,   is  a  scale   of  sines. 


288 


Disorders  of  Motility 


ular  vision  exists.  The  rings  shown  in  Fig.  130  are  typical  of  the 
diagrams  which  are  used  in  testing  the  sense  of  perspective.  When 
these  rings  are  fused  in  single  vision  they  give  the  impression  of 
a  hollow  cylinder. 

Tests  for  Cyclophoria 

If,  with  one  eye  closed,  we  hold  before  our  other  eye  a  double 
prism,  so  that  its  double  base-line  bisects  the  pupil,  and  then  look 


fig.  131 

Cyclo-phorometer    (Savage). 


through  the  prism  at  a  horizontal  black  line  on  a  white  ground  we 
see  two  parallel  lines.  If  we  now  open  the  other  eye  we  see  a 
third  line  between  the  other  two  lines.  If  the  meridional  adjust- 
ment of  the  eyes  is  perfect,  all  three  lines  will  be  parallel  and  hori- 
zontal ;  but  if  there  is  a  tendency  to  deviation  of  the  meridians 
from  the  proper  adjustment  the  third  line  will  be  obliquely  in- 
clined to  the  other  two  lines. 

We  may  also  use  the  Maddox  rod  for  finding  the  equilibrium! 


Optometry  of  the  Motor  Apparatus  ■        289 

of  the  meridians.  For  this  purpose  we  place  a  rod  vertically 
before  each  eye  (Fig.  131).  The  two  lines  of  light  as  seen 
through  the  rods  should  form  a  continuous  horizontal  line.  Any 
deviation  of  either  line  from  the  horizontal  plane  indicates  cyclo- 
phoria,  and  the  angle  through  which  the  rod  must  be  turned  in 
order  to  make  the  line  appear  horizontal  measures  the  cyclophoria. 


fig.  132 

Clinoscope    (Stevens). 

Another  device  available  for  measuring  cyclophoria  is  the 
clinoscope  of  Stevens  (Fig.  132).  This  is  a  contrivance  for 
examining  the  lines  known  as  Volkman's  disks  (Fig.  133).  One 
line  is  seen  with  one  eye,  the  other  line  with  the  other  eye.  The 
two  lines  are  adjusted  exactly  in  the  vertical  plane.  If  they  appear 
to  form  a  continuous  line  (Fig.  134)  in  the  vertical  plane  there 
is  no  cyclophoria.  //  they  appear  as  a  broken  line,  there  is  cyclo- 
phoria or  cyclotropia,  and  this  is  measured  by  turning  the  faulty 


:2go  Disorders  of  Motility 

appearing  line  until  it  appears  to  be  vertical.  A  scale  which  marks 
the  degree  through  which  the  line  is  turned  shows  the  amount  of 
cyclophoria. 


tB.MEYR0WIT2.NX 
FIG.     133 


E.BJUEYROWITZ.NJr: 
FIG.    134 


The  following  authorities  have  been  consulted  in  the  prep- 
aration of  the  foregoing  chapter : 

Stevens,  Motor  Apparatus  of  the  Eyes. 

Howe,  Muscles  of  the  Bye. 

Maddox,  Tests  and  Studies  of  the  Ocular  Muscles. 

Savage.  Ophthalmic  Myology;  and  Ophthalmic  Neuro- 
myology. 

Duane,  Extra-Ocular  Muscles,  Posey  and  Spiller's  Eye  and 
Nervous  System. 

Worth,  Etiology  and  Treatment  of  Squint. 

Priestley  Smith,  A  Tape  Measure  for  Strabismus,  Ophthal. 
Review,  1888. 

Javal,  Manuel  du  Strabisme. 

Fuchs,  Text  Book  of  Ophthalmology. 

Graefe,  Albrecht  von,  Ueber  Musculare  Asthenopie.  Arch, 
fur  Ophthal.,  1862. 

Graefe,  Alfred,  Motilit'dtsstorimgen. 


CHAPTER  XVII 


NON-PARALYTIC   DISORDERS   OF   EQUILIBRIUM 

Any  deviation  from  perfect  muscular  adjustment  constitutes 
muscular  imbalance.  Of  the  two  general  classes  of  muscular 
imbalance,  non-paralytic  and  paralytic,  we  devote  our  attention  in 
the  present  chapter  to  the  former  class. 

Excess  of  Convergence 

When  from  any  cause  the  eyes  tend  to  assume  a  degree  of 
convergence  greater  than  that  required  by  the  position  of  the 
point  of  fixation  an  abnormal  tax  is  imposed  upon  the  nervous 
system  in  order  that  the  visual  lines  may  be  maintained  in  the 
proper  directions  for  binocular  vision.  If  the  tendency  to  exces- 
sive convergence  is  considerable  the  great  and  continued  strain 
results  in  nerve  exhaustion,  and  beyond  a  certain  period  the  effort 
for  binocular  vision  cannot  be  maintained.  The  latent  condition 
of  esophoria  then  gives  place  to  manifest  error,  esotropia,  or 
convergent  strabismus,  and  vision  is  performed  with  one  eye, 
while  the  other  deviates  inward. 

Latent  excess  of  convergence  may,  therefore,  be  converted 
into  manifest  strabismus  at  certain  times  as  when  the  eyes  are  tired 
from  prolonged  use,  and  especially  in  near  vision,  when  spasm 
of  convergence  is  frequently  incited  through  the  association  of 
accommodation.     In  such  cases  the  strabismus  is  intermittent. 

But  when  the  effort  necessary  for  binocular  vision  is  very 
great  or  when  the  fusion-impulse  is  weak,  it  usually  happens  that 
the  child  {for  convergent  strabismus  almost  always  develops  in 
childhood),  having  once  learned  the  art  of  squinting  with  monoc- 
ular vision,  will  altogether  abandon  the  effort  to  maintain  proper 
convergence.  The  strabismus  thus  becomes  constant  or  perma- 
nent. 

If  the  vision  is  equally  good  in  the  two  eyes,  either  eye  may  be 
used  for  fixation  while  the  other  squints  (  alternating  strabismus). 
But,  as  a  rule,  in  strabismus  one  eye  will  be  preferred  to 
the  other,  and  fixation  will  be  performed  always  with  the  better 

291 


292  Disorders  of  Motility 

eye,  while  the  inferior  eye  falls  into  a  state  of  permanent  devia- 
tion. Although  thus  apparently  confined  to  one  eye,  this  kind  of 
strabismus  is  not  a  monocular  affection.  The  excessive  conver- 
gence is  effected  by  innervation  of  both  internal  recti ;  but  in  order 
that  the  visual  line  of  the  fixing  eye  may  be  properly  directed, 
adduction  of  this  eye  is  prevented  by  suitable  innervation  of  its 
external  rectus,  just  as  when  convergence  is  maintained  together 
with  a  lateral  deviation  of  the  two  eyes  (Landolt).  In  strabismus 
this  is  usually  effected  by  turning  the  head  to  one  side. 

Although  the  convergence  is  always  in  excess  of  the  appro- 
priate amount,  it  diminishes  or  increases  with  the  recession  or 
approach  of  the  object  of  fixation;  moreover,  the  convergence- 
excess  remains  undisturbed  throughout  the  field  of  fixation,  for 
the  two  eyes  move  together  in  all  directions.  In  this  respect 
non-paralytic  differs  from  paralytic  strabismus,  and  it  is  because 
of  this  freedom  of  movement  that  the  former  is  called  concomi- 
tant strabismus. 

In  recently  formed  concomitant  strabismus  there  is  no  abnor- 
mal limitation  of  the  field  of  fixation  in  any  direction,  but  when 
from  long-continued  overaction  the  internal  recti  have  become 
permanently  shortened  while  the  external  recti  have  become 
correspondingly  weakened,  the  power  of  abduction  (external 
rotation)  falls  appreciably  below  that  of  the  normal  eye;  and 
since  the  internal  rectus  of  the  deviating  eye  is  the  muscle  which 
undergoes  the  greater  shortening,  the  external  rotation  of  this  eye 
is  not  infrequently  less  extensive  than  that  of  the  other  eye. 

Etiology  of  Excessive  Convergence. — We  have  learned 
that  through  the  variation  in  the  relative  accommodation  and  con- 
vergence distinct  binocular  vision  is  possible  in  ametropia.  The 
relation  between  accommodation  and  convergence  may  be  so 
modified  by  long  association  that  orthophoria  coexists  with  ame- 
tropia; or  the  orthophoric  condition  may  not  be  attained,  but 
whatever  imbalance  remains  may  be  latent.  In  hyperopia  the 
tendency  is  towards  excessive  convergence,  since  the  inordinately 
great  accommodative  effort  required  for  distinctness  of  images 
provokes  an  abnormally  great  convergence  impulse. 

In  childhood  convergence  is  especially  easy,  owing  to  the 
smallness  of  the  eyes  and  the  shortness  of  the  interocular  distance. 
Because  of  this  facility  for  convergence  and  of  the  irritation  trans- 
mitted   from   the  accommodation   center,   the   internal   recti   are 


Non-Paralytic  Disorders  of  Equilibrium  293 

thrown  into  a  spasmodic  condition  in  convergent  strabismus, 
whereby  the  degree  of  strabismus  is  increased.  This  spasm  of 
convergence  gradually  gives  place  to  anatomical  shortening  of  the 
internal  recti  muscles,  and  especially  of  the  internal  rectus  of  the 
deviating  eye. 

Spasm  of  convergence  has  also  been  attributed  to  a  number 
of  other  causes  (corneal  inflammations,  etc.),  but  for  the  most 
part  without  sufficient  reason.  It  may,  however,  be  due  to 
hysteria  or  to  other  nervous  hypersensitiveness. 

The  relative  strength  and  the  position  of  scleral  attachment 
of  the  internal  as  compared  with  the  external  recti  muscles  must 
also  be  regarded  as  a  factor  in  determining  the  predominance  of 
convergence  over  divergence. 

Defective  development  of  the  cerebral  fusion  centers  is, 
doubtless,  an  important  factor  in  the  etiology  of  convergent  stra- 
bismus. In  certain  cases  of  intractable  alternate  strabismus  with 
normal  visual  acuity  in  each  eye  we  may  reasonably  assume  that 
there  is  a  congenital  absence  of  the  fusion  faculty,  but  in  a  much 
larger  proportion  of  cases  there  are  other  factors  to  be  considered 
which  militate  against  the  post-natal  development  of  this  innate 
faculty.  The  more  important  of  these  contributing  causes  have 
been  mentioned  in  the  chapter  on  Hyperopia. 

Symptoms  of  Excessive  Convergence. — Slight  esopho- 
ria  may  give  rise  to  no  disturbance  whatever.  Higher  degrees 
cause  the  group  of  symptoms  which  have  been  described  as  asthe- 
nopia. The  least  amount  of  esophoria  which  may  produce 
asthenopic  symptoms  cannot  be  definitely  stated,  since  this  varies 
with  the  resisting  power  of  the  nervous  system.  In  general,  we 
may  say  that  an  amount  not  exceeding  3  A  at  six  meters  must 
be  placed  within  the  limits  of  normal  equilibrium. 

When  the  tendency  to  convergence  is  so  great  or  the  fusion 
impulse  so  weak  that  the  proper  directions  of  the  visual  lines 
cannot  be  maintained — that  is,  when  esophoria  passes  into  esotro- 
pia or  convergent  strabismus — muscular  asthenopia  is  replaced  by 
a  new  train  of  symptoms  which  originate  from  the  loss  of  binoc- 
ular single  vision. 

Deviation  of  the  N on- fixing  Eye. — The  inward  deviation 
of  the  cornea  of  the  non-fixing  eye  is  the  characteristic 
objective   symptom    of    convergent    strabismus.     This    deviation 


294  Disorders  of  Motility 

may  be  so  slight  as  to  be  unnoticeable  on  casual  observation,  but 
usually  it  is  apparent  at  a  glance. 

Diplopia. — In  permanent  non-paralytic  convergent  strabis- 
mus diplopia  is  not  a  common  symptom  because  of  the  early  age 
at  which  this  kind  of  strabismus  develops.  Diplopia  may  be 
demonstrated  in  some  cases  of  long  continuance,  but  more  fre- 
quently that  part  of  the  retina  upon  which  the  false  image  falls 
fails  to  transmit  stimulation  to  the  centers  of  consciousness.  This 
loss  of  function  results  from  the  cultivated  power  of  disregarding 
the  false  image.  That  part  of  the  retina  which  has  acquired  this 
insensitiveness  is  called  the  region  of  exclusion. 

In  certain  cases  there  appears  to  have  developed  a  new  asso- 
ciation of  nerve  fibers  whereby  the  false  image  is  fused  with  the 
true  image,  the  former  being  assigned  its  correct  position  in  space. 
In  these  cases  a  temporary  diplopia  occurs  after  a  successful 
operation  for  the  strabismic  defect. 

Amblyopia  Ex  Anopsia. — The  visual  acuity  of  the  deviat- 
ing eye  is  much  reduced  in  all  long-standing  cases  of  permanent 
non-paralytic  convergent  strabismus.  In  most  of  these  cases 
the  vision  of  the  squinting  eye  was  doubtless  defective  prior 
to  the  occurrence  of  strabismus,  the  defective  vision  being  the 
determining  cause  of  the  strabismus ;  but  abundant  observation 
has  shown  that  squinting  eyes  which  possessed  good  visual  power 
in  early  life  have  so  far  deteriorated  after  long-continued  disuse 
as  even  to  lose  the  power  of  fixation. 

Notwithstanding  the  inferiority  of  vision  of  the  squinting 
eye.  this  eye  is  still  of  material  assistance  in  extending  the  field 
of  vision.  It  is  significant  also  that  the  extreme  inner  part  of  the 
retina,  corresponding  to  the  temporal  field  on  the  affected  side, 
does  not  suffer  the  deterioration  which  involves  the  macular 
region. 

Diagnosis  of  Excessive  Convergence. — We  make  the 
diagnosis  of  excessive  convergence  by  the  application  of  the 
various  equilibrium  tests  which  were  described  in  the  preceding 
chapter.  We  distinguish  between  comitant  and  paralytic  affec- 
tions by  noting  whether  the  imbalance  exists  in  all  or  only  in  cer- 
tain directions  of  the  gaze. 

Treatment  of  Excessive  Convergence. — The  treatment 
of  esophoria  and  convergent  strabismus,  in  so  far  as  this 
consists  in  the  correction  of  any  causative  refractive  error,  has 


Non-Paralytic  Disorders  of  Equilibrium  295   ,  v 

been  considered  in  previous  chapters.  When  this  correction, 
together  with  hygienic,  tonic  or  other  treatment  indicated  by  the 
systemic  condition,  fails  to  afford  relief,  other  methods  must  be 
adopted. 

Prismatic  Glasses. — A  prism,  base  out,  before  each  eye, 
may  enable  the  eyes  to  retain  binocular  single  vision,  while  the 
visual  lines  assume  the  excessive  convergence  which  is  evoked 
by  the  muscular  balance.  In  this  way  diplopia  and  its  alternative, 
excessive  nervous  strain  to  maintain  proper  convergence,  may  be 
avoided,  and  consequently  subjective  disturbance  may  be  thus 
relieved.  But  this  method  has  its  limitations,  for,  on  account  of 
the  distorting  property  of  prisms,  it  is  not  possible  to  wear  strong 
glasses  of  this  kind.  A  strength  of  4A  for  each  eye  is  the  limit 
usually  assigned. 

In  the  application  of  this  method  it  is  usually  advisable  to 
correct  only  a  portion  of  the  esophoria,  a  prismatic  strength  of 
one-half  or  two-thirds  of  the  amount  manifested  at  six  meters 
being,  in  favorable  cases,  sufficient  to  relieve  the  asthenopia.  s 

Prisms  prescribed  for  the  relief  of  esophoric  asthenopia  must 
ordinarily  be  worn  constantly. 

In  minor  degrees  of  esophoria  relief  may  be  expected  from, 
the  use  of  prismatic  glasses;  but,  unfortunately,  in  many  cases  the- 
excess  of  convergence  is  so  great  that  only  a  small  portion  can 
be  corrected  within  the  limits  prescribed  for  such  glasses.  In 
some  cases,  also,  in  which  relief  is  at  first  afforded,  the  esophoria 
apparently  increases  under  the  relaxing  influence  of  the  prisms,, 
so  that  the  strength  of  the  latter  has  to  be  increased.  If  the  limit 
has  already  been  reached,  this  method  is  no  longer  applicable,* 

It  is  apparent  that  decentering  a  convex  lens  inward  or 
a  concave  lens  outward,  has  the  effect  of  adding  a  prism,  base  in, 
to  the  lens ;  while  decentering  a  convex  lens  outward  or  a  concave 
lens  inward  has  the  effect  of  adding  a  prism,  base  out. 

In  a  lens  of  1  D  a  ray  parallel  to  the  axis  and  passing  through 
the  lens  at  a  distance  of  1  cm  from  the  center,  is  deviated  I  cm 
in  reaching  the  focus  of  the  lens.  1  meter  distant ;  that  is,  for  this 
ray  the  lens  has  the  same  effect  as  a  prism  of  iA.  If  the  lens 
has  a  power  of  2  D  the  prismatic  effect  at  a  distance  of  1  cm 

*This  apparent  increase  in  the  esophoria  is  not  due  to  any  injurious  effect  of  the 
prisms.  On  account  of  a  spasmo'dic  condition  of  the  muscles,  or  an  over  excitation 
of  the  nerve  centers,  a  portion  of  the  esophoria  is  not  at  first  revealed;  but  under 
the  influence  of  the  prisms  the  eyes  gradually  assume  their  position   of  equilibrium. 


2g6  Disorders  of  Motility 

from  its  center  is  2 A,  and  so  on.  Therefore,  the  rule  is  that 
■dec entering  a  spherical  lens  (or  a  cylinder  at  right  angles  to  its 
axis)  produces  a  prismatic  effect  equal  to  as  many  prism  diopters 
as  there  are  diopters  in  the  lensi 

We  may  write  an  order  for  the  decentering  of  a  lens  in 
accordance  with  the  foregoing  rule,  or  we  may  order  the  required 
lens  plus  (-(-)  the  required  prism,  leaving  to  the  optician  the 
choice  between  decentering  and  grinding  the  spherical  curvature 
upon  the  face  of  the  prism.  But  here,  as  in  all  cases,  we  should 
test  the  accuracy  of  the  optician's  work  by  examining  the  glasses 
after  they  have  been  made.  We  may  determine  the  strength  of 
a  prism  by  neutralizing  the  displacement  with  a  prism  taken  from 
the  trial  case,  or  we  may  note  the  displacement  on  a  prism-diopter 
scale.  In  testing  a  sphero-prism  we  must  be  careful  to  measure 
the  prismatic  effect  at  the  center  of  the  lens. 

When  the  principal  plane  of  the  prism  is  to  be  placed  hori- 
zontally or  vertically,  the  simple  designation  base  in,  base  out, 
base  up,  or  base  doz^u  suffices  to  denote  the  desired  position ;  but 
when  the  principal  plane — or  the  base-apex  line — is  to  be  placed 
in  an  oblique  meridian,  we  denote  the  direction  of  the  principal 
plane  by  the  angular  marking  on  the  trial  frame. 

We  may,  if  we  so  desire,  replace  a  single  prism  in  an  oblique 
meridian  by  two  prisms  at  right  angles  to  each  other,  one  vertical 
and  the  other  horizontal.  We  may  thus  place  the  vertically  acting 
prism  before  one  eye  and  the  horizontally  acting  prism  before  the 
other  eye. 

Stereoscopic  Exercises. — In  convergent  strabismus  in  chil- 
dren if  the  deviation  is  not  promptly  overcome  by  the  correc- 
tion of  the  ametropia  we  should  attempt  to  incite  the  impulse  for 
binocular  vision  by  stereoscopic  exercises.  The  importance  of 
this  procedure  was  first  shown  by  3 aval. 

Various  special  forms  of  stereoscopes  and  of  pictures  have 
been  devised  for  the  cultivation  of  binocular  vision.  Of  these, 
Worth's  amblyoscope  is  perhaps  the  most  convenient,  in  that  with 
it  binocular  vision  is  possible  even  when  the  eyes  are  affected 
with  a  high  degree  of  strabismus.  This  instrument  is  also  well 
adapted  for  changing  the  intensity  of  illumination  on  one  side 
without  affecting  that  of  the  other  side,  so  that  by  means 
of  small  electric  lamps  the  child's  attention  may  be  attracted  to 


Non-Paralytic  Disorders  of  Equilibrium  297 

the  image  in  the  amblyopic  eye  by  making  the  illumination  more 
intense  for  this  eye  than  for  the  better  eye. 

In  those  cases  in  which  it  is  not  to  be  expected  that  stereo- 
scopic training  will  overcome  the  strabismus,  the  prolonged  daily 
use  of  such  exercises  with  the  amblyoscope  is  yet  of  very  great 
value  in  preventing  amblyopia  ex  anopsia  and  in  developing  the 
fusion  sense  while  awaiting  a  suitable  time  for  operative  meas- 
ures. The  same  exercises  are  likewise  useful  for  developing  the 
fusion  sense  and  inciting  binocular  vision  after  operative  meas- 
ures have  overcome  the  greater  part  of  the  strabismus. 

Worth  concludes,  as  the  result  of  the  examination  of  a  large 
number  of  children,  that  binocular  vision  is  first  attempted  about 
the  sixth  month  of  age,  and  that  the  development  of  the  fusion 
faculty  is  completed  by  the  end  of  the  sixth  year. 

This  constitutes  the  chief  obstacle  to  this  plan  of  treatment, 
since  the  very  young  children  for  whom  it  is  applicable  frequently 
fail  to  give  the  co-operation  necessary  for  success.  The  experi- 
ence of  Worth,  however,  shows  that  much  can  be  accomplished 
by  the  exercise  of  patience  and  care. 

Bar  reading  consists  in  making  use  of  a  device  which  requires 
the  use  of  both  eyes  in  reading,  as  when  we  hold  a  pencil  between 
the  eyes  and  the  printed  page.  This  plan  gives  a  simple  means  of 
exercising  the  amblyopic  eye,  but  unfortunately  it  is  not  applicable 
until  after  the  passing  of  the  age  which  offers  the  greatest  encour- 
agement for  the  institution  of  binocular  vision. 

Use  of  Atropin  and  Bandaging  in  Developing  the  Am- 
blyopic Eye. — In  those  cases  in  which  stereoscopic  exercises 
are  not  available,  the  amblyopic  eye  may  be  trained  by  bandag- 
ing the  better  eye  for  a  brief  period  once  or  twice  a  day,  so 
that  fixation  with  the  amblyopic  eye  is  necessitated.  The  use 
of  atropin  in  the  better  eye  is  also  of  material  assistance,  since  it 
compels  the  inferior  eye  to  be  used  for  near  vision. 

Prism  Exercises. — Exercising  the  diverging  power  consists 
in  having  the  patient  look  at  a  distant  point,  as  a  candle  flame, 
alternately  zvith  and  without  divergence-prisms  (bases  in),  these 
being  preferably  placed  in  a  spectacle  frame  and  raised  and  low- 
ered at  intervals  of  five  seconds  (Savage).  Those  who  advocate 
this  method  believe  that  the  rhythmical  contractions  thus  produced 
in  the  external  recti  strengthen  these  muscles  or  train  the  nerve 
centers  presiding  over  divergence  so  as  to  enable  them  to  over- 


298  Disorders  of  Motility 

come  the  excessive  convergence.  Opinions  differ  as  to  the  merits 
of  prism  exercise.  My  own  belief,  based  partly  upon  theoretical; 
grounds  and  partly  upon  practical  results,  is  that  it  is  of  no  value. 

Operative  Treatment. — When  all  other  measures  fail  to 
give  relief  either  in  esophoria  or  in  esotropia,  operative  treatment 
should  be  undertaken. 

The  operative  treatment  of  esophoria  consists  in  a  carefully 
guarded  tenotomy  of  the  internal  rectus  or  an  advancement  of  the 
external  rectus.  In  either  operation  it  is  preferable  to  divide  the 
effect  between  the  two  eyes  in  the  higher  degrees  of  esophoria.  Of 
these  two  operations  tenotomy  is  more  frequently  selected  as  being, 
the  simpler  and  less  painful  at  the  time  of  operation  and  during 
the  healing  process.  The  possibility,  however,  of  a  resulting  defi- 
ciency of  convergence,  as  sometimes  occurs,  leads  many  surgeons 
to  believe  it  more  rational  to  strengthen  the  weak  external  recti,  by 
advancement,  than  to  weaken  the  power  of  the  internal  recti. 

The  surgeon  may  be  aided  in  his  choice  of  an  operation  by 
examination  of  the  fields  of  fixation  and  of  the  power  of  con- 
vergence and  divergence.  When  the  esophoria  is  due  to  weakness 
of  divergence,  and  not  to  overaction  of  convergence — that  is,  when 
convergence  is  not  decidedly  greater  than  the  normal  amplitude — 
advancement  is  the  only  permissible  operation. 

The  operative  treatment  of  convergent  strabismus  likewise 
consists  in  tenotomy  of  the  internal  rectus  or  advancement  of  the 
external  rectus,  the  effect  being  preferably  divided  between  the 
two  eyes  except  in  the  lower  grades  of  strabismus.  When  the 
operation  is  to  be  performed  upon  only  one  eye  at  the  first  sitting, 
the  inferior  (squinting)  eye  should  always  be  selected. 

It  is  especially  in  the  extensive  tenotomies  undertaken  for  the 
cure  of  high  convergent  strabismus  that  subsequent  deformity  is 
liable  to  occur,  such  as  sinking  of  the  caruncle,  proptosis,  and  even 
extreme  divergence  with  marked  limitation  of  movement.  Hence, 
for  the  correction  of  those  cases  of  convergent  strabismus  in 
which  it  is  apparent  that  a  moderate  tenotomy  on  each  eye  will 
not  suffice,  an  advancement  of  the  external  rectus  combined  with 
the  tenotomy  must  be  undertaken,  the  effect  being  preferably 
divided  between  the  two  eyes. 

The  proper  age  for  operative  intervention  in  convergent  stra- 
bismus depends  upon  the  probability  of  obtaining  binocular  vision. 
If  the  operation  is  to  be  undertaken  solely  for  the  cosmetic  result,, 


Non-Paralytic  Disorders  of  Equilibrium  2gg 

vision  being  hopelessly  defective  in  the  squinting  eye,  the  proced- 
ure should  be  delayed  until  the  tenth,  or  twelfth  year,  or  even 
later,  since  in  a  small  proportion  of  cases  a  spontaneous  cure  of 
spasmodic  convergence  occurs  in  childhood.  If,  on  the  other 
hand,  stereoscopic  training  with  the  amblyoscope  evokes  a 
strong  desire  for  binocular  fusion,  an  early  operation  is  demanded 
(Worth),  provided  the  non-operative  methods  aforementioned 
have  proved  unsuccessful. 

For  a  description  of  the  technique  of  tenotomy  and  advance- 
ment operations  the  reader  is  referred  to  works  dealing  with 
ophthalmic  surgery. 

Deficiency  of  Convergence 

Deficiency  of  convergence  is  either  latent  or  manifest,  consti- 
tuting, respectively,  exophoria,  and  extropia  or  divergent  stra- 
bismus. 

As  in  excess  of  convergence,  so  in  deficiency  binocular  vision 
may  give  place  to  strabismus  with  monocular  vision  only  at  certain 
times,  as  when  the  eyes  are  exhausted  from  prolonged  use  (inter- 
mittent divergent  strabismus).  If  vision  is  equally  good  in  the 
two  eyes,  either  eye  may  be  used  for  fixation  while  the  other 
squints  (alternate  divergent  strabismus)  ;  but  if,  as  is  usually  the 
case,  the  vision  of  one  eye  is  inferior  to  that  of  the  other,  the 
strabismus  will  be  permanently  confined  to  the  inferior  eye  (per- 
manent divergent  strabismus). 

As  in  convergent  strabismus,  so  in  non-paralytic  divergent 
strabismus  the  conjugate  movements  are  preserved  throughout 
the  field  of  fixation  (concomitant  divergent  strabismus). 

Etiology  of  Convergence  Deficiency. — Myopia  as  a 
factor  in  the  production  of  exophoria  and  divergent  strabismus 
has  been  considered  in  Chapter  XII.  Myopia  bears  the  same  rela- 
tion to  deficiency  as  hyperopia  does  to  excess  of  convergence :  the 
weakness  of  the  accommodative  impulse,  the  elongation  of  the 
eyeballs,  and  the  proximity  of  the  farthest  point  of  distinct  vision, 
all  aid  in  rendering  convergence  difficult. 

Aside  from  the  myopic  condition,  non-paralytic  deficiency 
of  convergence  may  arise  from  overstrain  of  the  eyes  in  near 
work,  from  innate  preponderance  of  the  external  over  the  internal 


300  Disorders  of  Motility 

recti,  from  reduced  physical  vigor,  and  from  mechanical  impedi- 
ment (as  in  exophthalmos). 

Determining  Causes  of  Divergent  Strabismus. — The  de- 
velopment of  divergent  strabismus  from  exophoria  is  favored 
by  loss  or  deterioration  of  vision  of  one  eye,  and  by  so  high  a 
degree  of  myopia  that  the  convergence  required  for  binocular 
vision  is  difficult  or  impossible. 

Divergent  strabismus  is  ordinarily  a  condition  of  adult  life; 
more  rarely  it  develops  in  childhood,  as  in  congenital  myopia,  or 
in  high-grade  hyperopia. 

Symptoms  of  Convergence  Deficiency. — Insufficiency 
of  convergence  gives  rise  to  muscular  asthenopia,  especially  when 
the  eyes  are  tired  from  prolonged  near  work.  The  latter  is  some- 
times impossible,  so  great  is  the  disturbance  produced  by  it.  This 
disturbance  is  partly  a  symptom  of  overtaxation  of  the  conver- 
gence function;  but  in  the  worst  cases  confused  vision  (crossed 
diplopia)  from  the  impossibility  of  maintaining  convergence  is  the 
chief  factor. 

The  reasons  assigned  for  the  absence  of  diplopia  in  conver- 
gent strabismus  are  not  applicable  to  divergent  strabismus,  since 
this  develops  in  adult  life ;  but  diplopia  is  not  a  common  symptom 
in  the  latter  condition  either,  because  divergent  strabismus  usually 
develops  only  when  the  visual  acuity  of  one  eye  is  much  reduced, 
so  that  exclusion  of  the  false  image  is  quickly  learned.  In  those 
cases  in  which  both  eyes  possess  good  visual  acuity  diplopia  is  a 
troublesome  symptom  in  the  developmental  stage,  but  it  subse- 
quently disappears  or  ceases  to  give  annoyance.  The  power  of 
excluding  the  false  image  is  aided  by  the  position  of  extreme 
divergence,  which  is  on  this  account  frequently  induced,  for  when 
the  image  falls  upon  the  periphery  of  the  retina,  it  does  not  excite 
attention  so  readily  as  when  it  falls  near  the  macula. 

Diagnosis  of  Convergence  Deficiency. — We  make  the 
diagnosis  of  convergence  deficiency  and  the  distinction  between 
comitant  and  paralytic  imbalance  by  the  application  of  the  tests 
which  have  already  been  described. 

The  existence  of  exophoria,  as  thus  determined,  at  six  meters 
is  strong  evidence  that  the  converging  power  is  abnormally  weak ; 
but  the  converse  does  not  follow,  for  insufficient  convergence  for 
near  work  is  not  incompatible  with  orthophoria,  or  even  esophoria, 
in  distant  vision.     The   determining  test  consists   in  the  direct 


Non-Paralytic  Disorders  of  Equilibrium  301 

measurement  of  the  amplitude  of  convergence  with  the  ophthalmo- 
dynamometer. The  amplitude  required  depends  upon  the  kind 
of  work  pursued,  but  an  amount  less  than  8  ma,  which  corre- 
sponds to  a  near-point  of  five  inches,  is  insufficient  for  continuous 
reading  or  writing,  since  only  about  one-third  of  this  amplitude 
is  available  for  prolonged  use. 

It  is  in  this  condition  also,  as  in  excessive  convergence, 
important,  especially  in  regard  to  operative  treatment,  that  we 
measure  the  diverging  power  by  means  of  prisms. 

In  strabismus  the  angle  of  deviation  and  the  field  of  fixation 
should  be  measured  as  described  in  the  preceding  chapter. 

Treatment  of  Convergence  Deficiency. — The  impor- 
tance of  correcting  any  causative  refractive  error  is  apparent,  and 
has  been  sufficiently  considered  in  previous  chapters.  In  addition, 
avoidance  of  overuse  of  the  eyes  in  near  work  and  other  hygienic 
measures  must  be  inculcated,  according  to  the  necessities  of  the 
case. 

Prismatic  glasses  (bases  in)  are  useful,  within  the  limita- 
tions to  which  such  glasses  are  restricted,  for  the  relief  of  exo- 
phoric  asthenopia.  In  those  cases  in  which  asthenopia  arises  only 
after  prolonged  near  work,  the  glasses  may  be  worn  for  such 
work  only ;  but  when  there  is  marked  exophoria  at  six  meters, 
relief  is  usually  afforded  only  by  the  constant  use  of  the  glasses. 

As  in  excess  of  convergence,  so  in  deficiency  we  often  find 
that  prisms  which  for  a  time  relieve  the  asthenopic  symptoms  seem 
to  increase  the  heterophoria.  In  such  cases  if  the  limit  to  which 
prismatic  glasses  are  subject  has  been  reached,  operative  treat- 
ment may  be  required. 

Prism  Exercises. — Those  who  advocate  prism  exercise  in 
the  treatment  of  excess  recommend  it  also,  with  greater  confi- 
dence, in  deficiency  of  convergence.  The  method  of  application 
is  similar  to  that  used  in  excess  of  convergence,  except  that  the 
bases  of  the  prisms  are  reversed,  being  placed  towards  the  temples. 

Stereoscopic  Training. — Owing  to  the  circumstances  under 
which  divergent  strabismus  usually  develops,  training  with  the 
stereoscope  is  less  frequently  indicated  than  in  convergent  stra- 
bismus. Occasionally,  however,  when  the  impulse  for  binocular 
insion  is  feeble,  while  the  visual  acuity  in  each  eye  is  good,  stereo- 
scopic exercises,  either  alone  or  in  conjunction  with  surgical  treat- 
ment, may  prove  useful. 


302  Disorders  of  Motility 

Operative  Treatment. — For  the  relief  of  asthenopia  operative 
procedure  should  be  undertaken  only  after  all  other  measures 
have  proved  unsuccessful.  Of  the  two  operations — tenotomy  of 
the  external  and  advancement  of  the  internal  rectus — tenotomy  is 
the  simpler,  and  may  be  selected  in  appropriate  cases.  There  is 
less  danger  of  a  disastrous  result  from  a  properly  perfomed 
tenotomy  of  the  external  than  of  the  internal  rectus.  Ten- 
otomy should  not  be  selected,  however,  unless  the  prism  test 
shows  the  divergence  to  be  decidedly  in  excess  of  the  normal 
amount. 

In  strabismus  of  long  standing  simple  tenotomy  has  but  little 
effect  in  overcoming  divergence.  For  the  correction  of  such  cases 
advancement  (usually  on  both  eyes)  should  be  performed. 

Vertical   Imbalance 

In  convergent  strabismus  of  high  degree  there  is  usually 
superadded  an  upward  deviation  of  the  squinting  eye,  while 
divergent  strabismus  is  usually  complicated  with  downward  devia- 
tion. Aside  from  such  cases  non-paralytic  vertical  strabismus  is 
not  common.  Hypertropia,  though  usually  considered  with  comi- 
tant  errors,  is  probably  almost  always  of  paralytic  origin. 

Concomitant  hyperphoria  is,  on  the  other  hand,  quite  com- 
mon.    It  is  usually  of  low  degree,  iA  or  2  A. 

Etiology. — The  explanation  usually  given  for  the  occurrence 
of  hyperphoria  is  that  the  balance  of  power  between  the  elevator 
and  the  depressor  muscles  of  one  eye  differs  slightly  from  that 
of  the  other.  Stevens  regards  declination  of  the  retinal  meridians 
as  the  primary  error. 

Symptoms  and  Diagnosis. — Vertical  imbalance  may  cause 
asthenopia,  diplopia,  monocular  vision,  or  torticollis  from  com- 
pensatory obliquity  of  the  head.  We  make  the  diagnosis  of  hyper- 
phoria' by  the  application  of  one  or  more  of  the  equilibrium  tests 
already  described.  We  may  also  with  advantage  measure  the  power 
of  right  and  left  sursnmduction ;  that  is,  the  power  of  the  right  and 
left  eye,  respectively,  to  deviate  relatively  upward.  The  strongest 
prism,  base  down,  before  the  right  eye  or  base  up  before  the  left 
eye,  with  which  diplopia  can  be  overcome,  measures  right  sursum- 
duction.  Similarly,  the  strongest  prism,  base  down,  before  the 
left  eye  or  base  up  before  the  right  eye,  with  which  diplopia  can 


Non-Paralytic  Disorders  of  Equilibrium  303 

be  overcome,  measures  the  left  sursumduction.  In  normal  bal- 
ance sursumduction,  right  or  left,  is  about  2  A  (Stevens). 

A  higher  degree  of  sursumduction  for  one  eye  than  for  the 
•other  indicates  hyperphoria  of  the  eye  which  has  the  greater 
sursumduction.  In  order  to  determine  whether  the  relative  hyper- 
phoria is  due  to  overaction  of  the  elevator  muscles  of  the  higher 
eye  or  to  underaction  of  the  depressors  of  the  lower  eye,  recourse 
must  be  had  to  measurement  of  the  fields  of  fixation. 

Uncomplicated  vertical  strabismus  is  determined  by  the  tests 
which  reveal  hyperphoria,  and  in  addition  there  is  vertical  diplopia 
without  the  aid  of  the  horizontal  prism. 

Treatment. — Since  hyperphoria  does  not  reach  a  high 
degree  of  deviation,  the  asthenopia  to  which  this  imbalance  gives 
rise  may  in  favorable  cases  be  overcome  by  the  use  of  prismatic 
glasses.  The  strength  of  the  glass  should  ordinarily  be  divided 
between  the  two  eyes,  the  base  being  placed  down  before  the 
higher  eye  and  vice  versa.  The  same  proportion  of  error  (one- 
half  or  two-thirds)  should  be  corrected  as  has  been  recommended 
for  other  forms  of  heterophoria. 

The  concurrence  of  slight  hyperphoria  with  greater  lateral 
heterophoria  does  not  indicate  the  necessity  of  correcting  the 
vertical  error ;  at  least,  until  correction  of  the  lateral  imbalance 
has  failed  to  give  relief.  On  the  other  hand,  as  shown  by  Stevens, 
the  hyperphoria  is  in  some  cases  the  primary  defect,  the  lateral 
disturbance  being  produced  by  the  muscular  effort  to  overcome 
the  vertical  error.  When  it  becomes  necessary  to  correct  both 
lateral  and  vertical  heterophoria  the  equivalent  prism  and  the 
position  of  its  base  can  be  determined  in  accordance  with  instruc- 
tions given  in  Part  I  (p.  30)  ;  or  the  prism  before  one  eye  may  be 
used  to  correct  the  vertical  error  while  that  before  the  other  eye 
corrects  the  horizontal  error. 

If  prismatic  treatment  proves  unsuccessful  in  hyperphoria 
or  in  vertical  strabismus,  tenotomy  of  the  superior  rectus  of  the 
higher  eye  or  advancement  of  the  inferior  rectus  is  permissible, 
provided  the  symptoms  are  of  sufficient  gravity  to  justify  opera- 
tive interference.  But  here,  as  in  other  forms  of  heterophoria, 
we  must  bear  in  mind  that  the  existence  of  slight  or  even  con- 
siderable deviation  from  orthophoria  is  by  no  means  positive 
evidence  that  this  deviation  is  the  cause  of  headache  or  other 


304  Disorders  of  Motility 

reflex  disturbance.  If  prisms  do  not  afford  a  fair  measure  of 
relief  in  heterophoria,  except  in  the  highest  degree  of  lateral  in- 
sufficiency, it  may  reasonably  be  assumed  that  operative  treatment 
will  be  equally,  unsuccessful. 

Cyclophoria  and  Cyclotropia 

The  terms  cyclophoria  and  cyclotropia  (or  declination)  have 
already  been  described,  and  the  methods  of  detecting  such  anom- 
alies have  been  given. 

Cyclophoria,  being  a  latent  condition,  coexists  with  binocular 
vision,  and  may  therefore  give  rise  to  asthenopia. 

Cyclotropia,  being  a  manifest  imbalance,  occurs  in  certain 
forms  of  strabismus. 

Very  great  importance  is  attached  to  these  conditions  by 
Stevens  and  by  Savage,  who  have  devoted  much  study  to  the 
elucidation  of  this  very  difficult  subject.  While  the  mal-adjust- 
ment  of  the  retinal  meridians  is  doubtless  capable  of  causing  much 
physical  disturbance  in  those  cases  in  which  the  imbalance  is 
considerable,  my  experience  has  not  led  me  to  believe  that  cyclo- 
phoria is  a  common  contributing  element  in  the  etiology  of  asthe- 
nopic  symptoms. 

Treatment. — Savage  recommends  exercising  the  oblique 
muscles  with  cylindrical  lenses.  Stevens  advises  operative  treat- 
ment. This  consists  in  changing  the  position  of  attachment  of 
the  upper  or  lower  part  of  an  internal  or  external  rectus,  so  as 
to  secure  the  proper  rotation  of  the  eye  on  its  antero-posterior 
axis. 

Anophoria,  Anotropia;  Katophoria,   Katotropia 

These  rare  conditions  have  also  been  described  as  double 
vertical  strabismus.  In  anotropia,  when  either  eye  performs  fixa- 
tion, the  other  eye  deviates  upward ;  in  katotropia,  when  either 
performs  fixation,  the  other  eye  deviates  downward. 

In  anotropia  the  head  is  bent  forward,  and  in  katotropia  it  is 
bent  backward,  so  as  to  counteract  the  effect  of  the  deficient 
ocular  rotation. 

Prisms,  base  down,  before  each  eye,  in  upward  tendency 
and  base  up  before  each  eye  in  downward  tendency  may  be  of  use. 
Stevens,  who  regards  the  primary  trouble  as  an  error  of  declina- 
tion, recommends  operative  treatment. 


Non-Paralytic  Disorders  of  Equilibrium  305 

Spasmodic  Conjugate  Deviation 

Spasmodic  conjugate  deviation  sometimes  occurs  as  a  symp- 
tom of  irritative  cerebral  lesion,  being  the  condition  opposite  to 
paralytic  conjugate  deviation. 

Nystagmus 

Nystagmus  consists  in  a  rapid,  short,  oscillatory  motion  of 
the  eyes.  The  direction  of  motion  may  be  lateral  (horizontal 
nystagmus),  vertical  (vertical  nystagmus),  or  there  may  be  a 
rotary  motion  around  the  antero-posterior  axis  (rotatory  nystag- 
mus). The  last  variety  may  be  combined  with  horizontal  or 
vertical  motion  (mixed  nystagmus).  Both  eyes  are  affected, 
except  in  rare  instances.  The  nystagmus  is  more  pronounced  in 
some  positions  than  in  others,  being  worse  in  forced  positions  of 
the  eyes. 

Etiology. — Nystagmus  is  very  common  among  coal  miners, 
being  due  to  the  long-continued  use  of  the  eyes  in  forced  rotation 
obliquely  upward  (miners'  nystagmus). 

This  affection  also  occasionally  develops  in  adult  life  as  the 
result  of  cerebral  lesion  (disseminated  sclerosis). 

Aside  from  the  aforementioned  conditions,  nystagmus  almost 
always  dates  from  early  infancy.  It  occurs  when  the  vision  of 
both  eyes  is  so  highly  defective  that  the  impulse  for  macular  fixa- 
tion is  not  acquired.  It  does  not  occur  in  complete  blindness;; 
hence,  it  is  apparent  that  the  nystagmic  movements  are  in  some 
way  associated  with  the  effort  to  obtain  better  vision,  the  improve- 
ment of  vision  being  derived  from  these  movements  in  the  same 
way,  perhaps,  that  the  peripheral  field  of  vision  is  greater  when 
the  examiner  moves  the  test  object  to  and  fro  than  when  this 
object  is  held  motionless. 

Chief  among  the  causes  of  such  defective  vision  as  results  in 
nystagmus  are  the  complications  of  ophthalmia  neonatorum,, 
albinism,  congenital  opacity  of  the  cornea  or  lens,  and  sometimes, 
very  great  refractive  error. 

Very  rarely  congenital  nystagmus  has  been  found  to  coexist 
with  good  visual  acuity;  in  such  cases  the  movements  must  be 
attributed  to  some  anomaly  of  the  nerve  centers. 

Symptoms  and  Diagnosis. — In  nystagmus  which  arises 
in  infancy  there  are  no  subjective  symptoms  attributable  to  tho 
oscillatory  movements,  but  in  that  which  develops  in  adult  life  the 


306  Disorders  of  Motility 

motion  of  the  eyes  makes,  all  objects  appear  unsteady,  with  result- 
ing confusion  of  vision,  vertigo,  and  other  disturbances. 

The  diagnosis  of  nystagmus  is  readily  made  .from  visual  in- 
spection. Clonic  contractions  of  the  ocular  .muscles  occur  physio- 
logically when  the  attempt  is  made  to  hold  the  eyes  in  the  position 
of  maximum  rotation.  This  condition  should  not  be  mistaken  for 
nystagmus,  which  is  present  in  all  directions  of  the  gaze. 

1  . .  Treatment. — Miners'  nystagmus  is  cured  by  cessation  from 
coal-digging.  If  possible  a  permanent  change  of  occupation 
should  be  made,  since  the  disease  is  liable  to  return  on  renewal  of 
work  in  the  mines. 

Treatment  is  evidently  unavailing  in  nystagmus  which  re- 
sults from  incurable  lesion  of  the  brain  or  of  the  eyes.  Even  in 
those  cases  in  which  vision  can  be  improved  by  iridectomy  or 
other  surgical  procedure,  the  nystagmus  is  benefited  only  when 
the  operation  is  performed  at  an  early  age. 

Disorders  of  Motility  Caused  by  Mechanical  Impediment 

Limitation  of  ocular  movement  may  be  due  to  exophthalmos, 
orbital  tumor,  or  allied  condition.  Such  cases  require  no  special 
consideration  here,  the  disturbance  of  motility  being  of  secondary 
importance  in  comparison  with  the.  etiological  condition. 

Loss  of  function  is  also  produced  by  improperly  performed 
tenotomy  or  by  accidental  section  of  a  muscle  back  of  Tenon's 
capsule. 

The  following  authorities  have  been  consulted  in  the  prep- 
aration of  the  foregoing  chapter: 

Stevens,  Motor  Apparatus  of  the  Byes. 

Maddox,  The  Ocular  Muscles. 

Howe,  The  Muscles  of  the  Eyes. 

Duane,  Extra-Ocular  Muscles,  Posey  and  Spiller's  Eye  and 
Nervous  System. 

Landolt,  Anomalies  of  the  Motor  Apparatus  of  the  Eyes, 
Norris  and  Oliver's  System  of  Diseases  of  the  Eye. 

Worth,  Etiology  and  Treatment  of  Squint. 


Non-Paralytic  Disorders  of  Equilibrium  307 

Javal,  Manuel  du  Strabisme. 

Savage,     Ophthalmic    Myology,    and    Ophthalmic    Ncuro- 
Myology. 

Fuchs,  Text  Book  of  Ophthalmology. 

Donders,  Anomalies  of  Refraction  and  Accommodation. 

Prentice,    Metric    System    of    Numbering    and    Measuring 
Prisms,  Arch,  of  Ophthal.,  1890. 


CHAPTER  XVIII 


PARALYTIC  DISORDERS  OF  MOTILITY 

Paralytic  disturbance  of  function  may  be  due  to  lesion 
in  any  part  of  the  course  of  the  motor  nerves,  from  their  peri- 
pheral expansions  to  the  highest  centers  presiding  over  muscular 
action.  As  regards  the  motor  apparatus  of  the  eyes  such  dis- 
orders may  be  conveniently  divided  into  two  classes.  The  first 
class  includes  paralysis  arising  from  a  lesion  situated  anywhere 
in  the  course  of  the  nerve  from  its  peripheral  expansion  up  to 
and  including  the  nucleus  which  controls  monocular  muscular 
action.  The  second  class  embraces  those  rarer  cases  of  paralysis 
of  associated  movement,  due  to  lesion  of  the  centers  which  pre- 
side over  the  working  of  the  two  eyes  in  unison,  or  to  lesion  of 
the  higher  centers  or  of  the  fibers  which  convey  impulses  from 
these  centers  to  the  motor  centers. 

Paralyses  of  the  Ocular  Muscles 

In  the  first  class  of  paralytic  disorders,  the  loss  of  muscular 
power  is  absolute ;  that  is,  it  exists  equally  for  all  innervational 
impulses.  The  loss  of  power  may  be  partial  (paresis)  or  total 
(complete  paralysis). 

Paralysis  may  affect  any  one  of  the  ocular  muscles  singly,  or 
it  may  involve  a  group  of  muscles  of  one  eye,  or  one  or  more  of 
the  muscles  of  each  eye. 

The  external  rectus  and  the  superior  oblique  are  most  fre- 
quently singly  paralyzed,  since  each  of  these  muscles  has  its  inde- 
pendent nerve;  while  the  internal,  the  superior,  and  the  inferior 
recti,  and  the  inferior  oblique,  all  being  supplied  by  the  third 
nerve,  are  usually  involved  in  a  combined  paralysis.  Bnt  some- 
times these  muscles  also  are  singly  paralyzed. 

All  the  extrinsic  muscles  of  the  eye  may  be  paralyzed,  while 
the  iris  and  ciliary  muscle  are  unaffected,  since  the  nucleus  of 
these  intrinsic  muscles  is  anterior  to  that  of  the  extrinsic  muscles. 
Paralysis  of  this  kind  is  called  external  ophthalmoplegia  in  con- 
tradistinction to  internal  ophthalmoplegia,  which  affects  only  the 


Paralytic  Disorders  of  Motility  309 

iritic  and  ciliary  muscles.  Paralysis  of  both  interior  and  exterior 
muscles  constitutes  total  ophthalmoplegia. 

Congenital  paralysis  may  affect  all  the  muscles  of  the  eye, 
but  it  is  usually  confined  to  one  external  rectus,  or  to  the  two 
superior  recti  in  conjunction  with  ptosis.  In  these  cases  the 
paralysis  is  associated  with  failure  of  muscular  development,  but 
the  origin  of  the  disease  is  probably  nuclear. 

A  peculiar  and  rare  form  of  congenital  paralysis  consists  in 
a  loss  of  the  power  of  abduction,  associated  with  retraction  of  the 
eyeball  and  narrowing  of  the  palpebral  fissure  in  adduction. 

Ophthalmoplegic  migraine  (Charcot)  is  a  form  of  recurrent 
paralysis  attended  by  nausea,  and  headache  on  the  affected  side. 
The  disease  attacks  children  and  young  adults.  At  the  early 
stage  of  the  disease  the  muscles  regain  their  power  in  the  interval 
between  the  attacks,  which  may  last  from  a  few  days  to  several 
months,  but  later  a  permanent  paresis  results.  The  pathology  of 
this  affection  is  obscure.  The  third  nerve  is  the  usual  seat  of 
this  kind  of  paralysis,  but  a  few  cases  have  been  observed  in 
which  the  sixth  nerve  was  attacked. 

Etiology. — Oculo-muscular  paralysis  may  be  due  either  to 
intra-cranial  or  to  orbital  lesion.  Intra-cranial  paralysis  may  be 
again  divided,  in  accordance  with  the  site  of  the  lesion,  into 
nuclear,  fascicular,  and  basilar.  The  most  common  cause  of 
intra-cranial  paralysis  is  syphilis,  the  gummatous  deposit  of  which 
produces  pressure  upon  the  nerves  or  their  nuclei.  The  principal 
other  causes  are  brain  tumor,  meningitis,  aneurism,  hemorrhage, 
tabes  (usually  regarded  as  a  late  manifestation  of  syphilis),  dis- 
seminated sclerosis,  and  certain  diseases  which  are  especially 
liable  to  cause  injury  to  nerve  tissue,  as  diabetes  and  poisoning  by 
alcohol,  tobacco,  and  lead. 

Orbital  paralysis  may  result  from  diphtheria,  rheumatism, 
diabetes,  or  lead  poisoning,  from  orbital  tumor,  hemorrhage,  frac- 
ture or  exostosis  in  the  region  of  the  optic  foramen,  sinusitis,  etc. 

General  Symptoms. — There  are  six  important  general 
symptoms  of  oculo-muscular  paralysis :  limitation  of  movement, 
strabismus,  diplopia,  false  projection,  vertigo  and  unsteadiness  of 
gait,  and  oblique  position  of  the  head.  These  general  symptoms 
are  common  to  all  paralyses. 

Limitation  of  Movement. — The  rotative  power  of  the 
eye  is  always  abnormally  circumscribed  in  the  field  of  action  of 


310  Disorders  of  Motility 

the  paralyzed  muscle.  In  complete  paralysis  this  limitation  is 
readily  determined  by  directing  the  patient  to  follow  with  his  eyes 
(his  head  being  unmoved)  the  point  of  a  pencil  or  other  object 
moved  in  various  directions  before  the  eyes,  when  the  examiner 
will  notice  that  the  paralyzed  eye  fails  to  follow  the  other  in  cer- 
tain movements.  In  incomplete  paralysis  (paresis)  the  limitation 
of  movement  is  often  too  slight  to  be  thus  determined.  This  is 
especially  the  case  in  affection  of  the  oblique  muscles.  In  such 
cases  assistance  may  be  gained  from  the  measurement  of  the 
field  of  fixation  with  the  perimeter  or  with  the  tropometer. 

Paralytic  Strabismus. — This  differs  from  concomitant  stra- 
bismus in  that  the  latter  is  maintained  in  all  directions  of  the 
gaze,  while  the  former  is  manifested  only  when  the  object  of 
vision  lies  within  the  field  of  action  of  the  paralyzed  muscle. 
Thus,  in  paralysis  of  the  left  external  rectus  the  right  eye  will 
properly  fix  an  object  situated  on  the  left  side,  but  the  left  eye 
cannot  be  turned  in  this  direction;  consequently  there  will  result 
a  convergent  strabismus  of  the  left  eye.  When,  however,  the 
gaze  is  directed  straight  forward  the  strabismus  becomes  less 
marked,  or  in  paresis  it  may  vanish,  giving  place  to  binocular 
fixation,  as  it  will  also  do  in  complete  paralysis  when  the  object 
is  moved  to  the  extreme  right. 

P>etween  paralytic  and  concomitant  strabismus  there  is  also 
another  point  of  difference  which  is  of  diagnostic  importance :  in 
concomitant  strabismus  the  angular  deviation  of  the  non-fixing 
eye  is  the  same,  whether  one  or  the  other  eye  is  used  for  fixation ; 
but  in  paralytic  strabismus  the  deviation  of  the  paralyzed  eye 
(primary  deviation)  when  the  sound  eye  is  fixing  is  less  than 
the  deviation  of  the  sound  eye  (secondary  deviation)  when  the 
paralyzed  eye  performs  fixation. 

The  explanation  of  the  greater  secondary  than  primary  devi- 
ation in  paralysis  is  to  be  found  in  the  binocular  innervation  of 
the  associated  muscles  involved  in  fixation.  Owing  to  the  dim- 
inution of  oower  of  the  paralyzed  muscle,  a  very  strong  impulse 
is  required  to  enable  the  affected  eye  to  move  into  the  fixation 
position — as  great  an  impulse  as  would  be  required  in  a  state  of 
health  to  effect  extreme  rotation.  This  strong  impulse  is  equally 
conveyed  to  the  associated  sound  muscles  of  the  other  eye,  and 
a  proportionately  strong  contraction  results. 

Diplopia. — This  is  the  most  prominent   subjective   symptom 


Paralytic  Disorders  of  Motility  311 

of  paralysis  developing  in  the  muscle  of  an  eye  whose  visual  acuity 
is  good.  The  diplopia  occurs  coincidently  with  the  strabismus ;  that 
is,  it  is  manifested  whenever  the  gaze  is  directed  towards  the  field 
of  action  of  the  paralyzed  muscle.  The  patient  may  himself  he 
aware  of  the  existence  of  diplopia,  or  he  may  complain  only  of 
confused  vision. 

The  analysis  of  diplopia  is  of  the  greatest  diagnostic  import- 
ance, for  it  is  from  the  relative  position  of  the  true  and  the  false 
image  and  from  the  direction  of  the  gaze  in  which  diplopia  occurs 
that  the  seat  of  paralysis  is  most  readily  determined  in  those 
cases  in  which  the  limitation  of  movement  is  too  slight  to  be 
apparent. 

False  Projection. — We  have  learned  in  the  study  of  con- 
comitant strabismus  that  the  false  image  is  improperly  projected, 
so  that  homonymous  or  crossed  diplopia  results  according  as  the 
strabismus  is  convergent  or  divergent.  The  same  error  is  made 
in  paralytic  strabismus ;  but  in  addition  there  is  another  kind  of 
false  projection  which  occurs  when  the  paralyzed  eye  is  perform- 
ing fixation,  the  sound  eye  being  covered.  This  false  projection 
is  due  to  the  muscular  sense,  which  enters  largely  into  the  judg- 
ment as  to  the  position  of  an  object  relatively  to  the  body.  We 
know  that  a  strong  impulse  is  required  in  order  to  perform  fixa- 
tion of  an  object  situated  to  the  extreme  right  (for  instance). 
If  the  right  external  rectus  is  paralyzed,  it  will  require  just  as 
great  an  impulse  for  the  right  eye  to  fix  an  object  situated  slightly 
to  the  right  as  would  be  required  to  effect  extreme  rotation  to 
the  right  in  a  healthy  eye.  Hence,  if  the  subject  of  such  paralysis, 
having  his  sound  eye.  covered,  is  asked  to  look  at  an  object 
situated  on  his  right  and  then  to  point  quickly  with  his  finger 
towards  the  object,  he  will  point  too  far  to  the  right,  because  of 
the  great  innervation  necessary  to  produce  the  requisite  action  of 
the  paralyzed  external  .rectus.  But  in  a  moment,  when  he  sees 
his  finger  pointing  in  the  wrong  direction,  he  will  rectify  his  error. 
This  is  called  Graefe's  touch  test. 

Vertigo  and  Unsteadiness  of  Gait. — These  disturbances  are. 
the  direct  result  of  the  diplopia  and  false  projection.  They  dis- 
appear upon  closure  of  the  paralyzed  eye. 

•  Oblique  Position  of  the  Head. — This  characteristic  symptom 
results  from  the  endeavor  to  avoid  diplopia  by  turning  the  head 


312  Disorders  of  Motility 

towards  the  field  of  action  of  the  paralyzed  muscle.    The  rotation 
of  the  head  thus  supplants  that  of  the  eyes. 

Symptoms  in  Old  Paralysis. — The  foregoing  symptoms  be- 
come less  characteristic  the  longer  the  paralysis  has  existed.  The 
strabismus  usually  increases  from  contraction  of  the  antagonistic 
muscles,  and  thus,  existing  to  some  extent  throughout  the  field  of 
iixation,  it  simulates  concomitant  strabismus.  Diplopia  ceases  to 
give  annoyance  or  it  even  disappears  entirely  if  the  habit  of  ex- 
clusion is  acquired.  False  projection  also  disappears,  since  it  is 
learned  that  an  exaggerated  impulse  corresponds  to  only  a  mod- 
erate movement.  With  the  disappearance  of  diplopia  and  false 
projection  vertigo  also  vanishes. 

Paralysis  of  the  External  Rectus  (Sixth  Nerve). — 
The  special  symptoms  which  characterize  this  paralysis  are 
inability  to  rotate  the  eye  outward  (abduction),  convergent 
strabismus,  homonymous  diplopia  (Fig.  135),  and  rotation  of 
the  head  towards  the  paralyzed  side,  and  false  projection  towards 
this  side.  These  symptoms  are  most  pronounced  when  the  object 
of  vision  lies  on  the  side  corresponding  to  the  affected  side,  and 
they  vanish  when  the  object  is  moved  to  the  extreme  opposite 
side. 

Paralysis  of  the  Internal  Rectus. — The  character- 
istics of  this  paralysis  are  limitation  of  internal  rotation  (adduc- 
tion), divergent  strabismus,  crossed  diplopia  (Fig.  136),  turning 
of  the  head  towards  the  sound  side,  and  false  projection  towards 
this  side.  The  symptoms  are  most  pronounced  when  the  object 
•of  vision  lies  on  the  side  corresponding  to  the  sound  eye,  and  they 
vanish  when  the  object  is  moved  to  the  extreme  opposite  side. 

Paralysis  of  the  Superior  Rectus. — The  external  and 
internal  recti  rotate  the  eyeball  around  a  single  (vertical)  axis 
when  the  object  of  vision  is  on  a  level  with  the  eyes,  and  conse- 
quently the  resulting  homonymous  or  crossed  diplopia  is  simple ; 
that  is,  the  two  images  are  on  the  same  level  and  parallel.  But 
the  action  of  all  the  other  ocular  muscles  is  more  complex,  as 
referred  to  the  three  primary  axes,  and  paralysis  of  these  muscles 
is  attended  by  a  more  complicated  relation  between  the  true  and 
false  image  than  follows  paralysis  of  the  external  or  internal 
rectus. 

The  superior  rectus  turns  the  eye  directly  upward  only  when 
the  eye  is   simultaneously  abducted  to  such  a  degree  that  the 


Paralytic  Disorders  of  Motility 


313 


antero-posterior  diameter  lies  in  a  straight  line  with  the  line  of 
action  of  the  muscle.     When  the  gaze  is  directed  straight   for- 


Paralysis  of 
left   eye. 


Paralysis  of 
left  eye. 


FIG.    135 
Paralysis  of  External   Rectus 


Lateral     separation     of     images 
looking  towards  the  paralyzed  side. 


increases 


Paralysis  of 
left  eye. 


FIG.    136 

Paralysis   of   Internal    Rectus 
Lateral     separation     of     images     increases     in 
looking   towards    the    sound    side. 


Paralysis   of 
left  eye. 


FIG.    137 

Paralysis  of   Superior  Rectus 

Vertical  separation  increases  in  elevation 
and  abduction.  Lateral  separation  diminishes  in 
abduction.     Obliquity  increases  in  adduction. 


FIG.    I38 

Paralysis  of  Inferior   Rectus 

Vertical  separation  increases  in  depression  and 
abduction.  Lateral  separation  diminishes  in  abduc- 
tion.     Obliquity   increases  in   adduction. 


Paralysis  of 
left   eye. 


FIG.    139 

Paralysis     of     Inferior     Oblique 
Vertical   separation   increases   in   elevation   and 
adduction.     Lateral  separation  diminishes  in  adduc- 
tion.     Obliquity    increases    in    abduction. 


Paralysis  of 
left   eye. 


FIG.    140 
Paralysis    of    Superior    Oblique 
Vertical     separation     increases     in     depression 
and    adduction.      Lateral    separation    diminishes    in 
adduction.      Obliquity    increases    in    abduction. 


Paralysis  of 
right   eye. 


Paralysis  of 
right    eye. 


Paralysis  of 
right   eye. 


Paralysis  of 
right   eye. 


Paralysis  of 
right   eye. 


Paralysis  of 
right  eye. 


3 14  Disorders  of  Motility 

ward,  the  action  of  the  muscle  is  divided  between  elevation,  ad- 
duction, and  rotation  of  the  cornea  about  the  antero-posterior 
axis,  and  the  last-named  action  increases  at  the  expense  of  the 
others  as  the  adduction  is  increased.  Hence,  it  is  only  in  the 
first-mentioned  position  that  paralysis  of  the  superior  rectus  is 
accompanied  by  simple  vertical  diplopia ;  in  other  directions 
of  the  gaze  the  false  image  is  displaced  both  vertically  and  later- 
ally, and  is  obliquely  inclined  to  the  true  image  because  of  the 
rotation  of  the  meridians  of  the  eye. 

In  paralysis  the  displacement  of  the  false  image  always  cor- 
responds to  the  direction  of  normal  action  of  the  paralysed  muscle, 
for  the  paralysis  is  followed  by  a  turning  of  the  eyeball  opposite 
to  that  of  the  normal  muscular  action,  and  we  know  that  the  false 
image  is  displaced  in  a  direction  opposite  to  the  turning  of  the  eye. 

Since  the  superior  rectus  turns  the  eye  upward  and  inward 
and  rotates  the  upper  end  of  the  vertical  meridian  inward,  the 
false  image  must  occupy  the  position  represented  in  Fig.  137; 
that  is,  the  diplopia  is  crossed,  and  the  false  image  is  above  the 
true  image,  the  lower  extremity  of  the  former  being  inclined 
towards  the  latter.  The  lateral  separation  of  the  images  dimin- 
ishes in  abduction,  the  obliquity  is  least  in  abduction  and  greatest 
in  adduction,  and  the  vertical  separation  is  greatest  in  looking 
upward. 

The  other  symptoms,  limitation  of  movement  upward  and 
inward,  downward  strabismus,  and  false  projection  require  no 
special  mention.  The  head  is  usually  inclined  backward  and 
towards  the  shoulder  of  the  healthy  side. 

Paralysis  of  the  Inferior  Rectus. — What  has  been 
said  of  the  superior  rectus  applies  equally  to  the  inferior  rectus, 
with  the  modification  that  the  inferior  rectus  draws  the  eye  down- 
ward and  inward  and  rotates  the  upper  end  of  the  vertical  merid- 
ian outward ;  hence,  in  looking  forward  and  downward  there  is 
slightly  crossed  diplopia,  the  false  image  being  below  the  true 
image,  and  having  its  upper  end  inclined  towards  the  true  image 
(Fig.  138).  The  vertical  separation  diminishes  on  looking 
upward,  the  lateral  separation  diminishes  in  abduction,  and  the 
obliquity  is  least  in  abduction  and  greatest  in  adduction. 

The  limitation  of  movement  is  downward  and  inward,  the 
strabismus  upward  and  outward,  and  the  inclination  of  the  head 
downward  and  towards  the  shoulder  of  the  paralyzed  side. 


Paralytic  Disorders  of  Motility  315'. 

Paralysis  of  the  Inferior  Oblique. — The  inferior  oblique 
turns  the  eye  upward  and  outward  and  inclines  the  upper 
end  of  the  vertical  meridian  outward ;  hence,  the  false  image  is 
displaced  upward  and  outward  (that  is,  homonymously ) ,  and  its- 
upper  extremity  is  inclined  away  from  the  true  image  (Fig.  139). 
The  vertical  separation  of  the  images  increases  when  the  patient 
looks  upward  and  towards  the  sound  side  (adduction )  ;  the 
obliquity  increases  when  he  looks  towards  the  paralyzed  side 
(abduction)  ;  the  lateral  separation  diminishes  in  adduction. 

The  limitation  of  movement  is  upward  and  outward,  the 
strabismus  is  slightly  downward  and  inward,  and  the  rotation  of 
the  head  upward  and  towards  the  paralyzed  side,  and  inclined 
to  the  shoulder  of  this  side. 

Paralysis  of  the  Superior  Oblique. — The  superior 
oblique  turns  the  eye  downward  and  outward  and  rotates  the 
upper  end  of  the  vertical  meridian  inward ;  hence,  the  false  image 
is  displaced  downward  and  outward  (homonymously),  and  its 
upper  extremity  is  inclined  towards  the  true  image  (Fig.  140). 
The  vertical  separation  of  images  increases  in  looking  downward 
and  towards  the  sound  side  (adduction)  ;  the  obliquity  increases 
in  looking  towards  the  paralyzed  side  (abduction)  ;  the  lateral 
separation  diminishes  in  adduction. 

There  is  slight  limitation  of  movement  downward  and  out- 
ward, with  a  corresponding  strabismus  upward  and  inward.  The 
rotation  of  the  face  is  downward  and  towards  the  paralyzed  side, 
with  the  head  inclined  towards  the  shoulder  of  the  sound  side. 

Paralysis  of  the  Third  Nerve. — Paralysis,  either  com- 
plete or  partial,  of  all  the  muscles  supplied  by  the  third  or 
oculomotor  nerve  is  more  common  than  paralysis  limited  to  one 
of  these  muscles.  In  complete  paralysis  the' appearance  is  un- 
mistakable :  the  eye.  being  subjected  to  the  unopposed  action  of 
the  external  rectus  and  the  superior  oblique,  is  deviated  outward 
and  downward,  the  upper  lid  droops  over  the  eye  (ptosis),  there 
is  mydriasis  and  cycloplegia  (if  the  intrinsic  muscles  are  in- 
volved), and  not  infrequently  proptosis  is  present,  because  of  the 
relaxation  of  the  recti  muscles,  which  normally  draw  the  eyeball 
into  the  orbit. 

Since  the  eye  is  drawn  outward  and  slightly  downward,  hav- 
ing the  upper  end  of  its  vertical  meridian  inclined  inward,  the 
false   image  must  be   displaced   inward    (crossed   diplopia)    and 


316  Disorders  of  Motility 

upward,  while  its  upper  extremity  is  inclined  towards  the  true 


image. 


The  effect  of  varying  the  direction  of  the  gaze  requires  no 
special  consideration,  in  view  of  what  has  already  been  said  in 
regard  to  paralysis  of  the  individual  muscles.  The  head  is  turned 
towards  the  sound  side,  and  is  inclined  towards  the  shoulder  of 
the  paralyzed  side ;  the  head  is  also  thrown  back  in  order  to 
supplant  the  deficient  downward  rotation,  and  to  compensate  for 
the  inability  to  raise  the  upper  lid. 

In  incomplete  paralysis  ptosis  may  not  be  present,  and  the 
other  symptoms  (including  the  diplopia)  are  modified  in  accord- 
ance with  the  extent  to  which  the  various  muscles  are  affected. 

Combined  Paralysis  of  the  Ocular  Muscles. — Several 
or  all  of  the  motor  nerves  of  the  eye  may  be  simultaneously 
paralyzed,  either  from  peripheral  or  nuclear  lesion.  Thus 
a  nuclear  paralysis  of  the  third  nerve  is  not  infrequently  asso- 
ciated with  paresis  of  the  fourth  and  sixth  nerves,  as  is  mani- 
fested by  deficient  action  of  the  superior  oblique  and  external 
rectus  in  conjunction  with  third  nerve  paralysis.  By  a  further 
extension  of  the  disease  process  the  paresis  of  these  two  nerves 
may  develop  into  complete  paralysis,  thus  causing  absolute  im- 
mobility of  the  eyeball.  Similarly,  the  adjoining  nuclei  of  the 
nerves  of  the  other  eye  may  be  attacked,  with  resulting  paresis 
or  paralysis  of  some  or  all  of  the  muscles  of  this  eye. 

Diagnosis. — The  existence  of  paralysis  of  an  ocular  muscle 
is  suspected  when  a  patient  complains  of  confused  vision,  vertigo, 
and  uncertainty  of  gait,  and  when  in  addition  it  is  noticed  that 
he  does  not  direct  his  gaze  straight  forward,  but  turns  his  head 
towards  one  side,  inclining  it,  perhaps,  at  the  same  time  towards 
one  shoulder.  In  such  a  case  the  suspected  diagnosis  is  con- 
firmed if  direct  inspection  reveals  limitation  of  movement  and 
strabismus,  the  latter  appearing  or  disappearing  according  as  the 
gaze  is  directed  towards  or  away  from  the  field  of  action  of  the 
affected  muscle.* 

But  in  the  more  common  condition  of  paresis  of  one  or 
more  of  the  muscles  the  limitation  of  movement  cannot  usually 
be  determined  by  simple  inspection.     The  appearance  of  slight 


*Loss   of   movement   due   to   section    of   a   muscle   may   be   excluded   by   the    history 
of  the   case. 


Paralytic  Disorders  of  Motility  317 

strabismus  is  also  liable  to  be  deceptive,  for  apparent  strabismus 
is  not  infrequently  coexistent  with  binocular  single  vision. 

If  the  strabismus  is  only  apparent,  binocular  fixation  may 
be  demonstrated  by  the  cover  test  and  by  the  other  methods 
enumerated  in  Chapter  XVI.  If  real  strabismus  is  revealed  by 
these  tests,  paralytic  is  distinguished  from  concomitant  strabismus 
in  accordance  with  the  characteristics  of  each ;  but  in  the  exact 
diagnosis  of  the  degree  and  seat  of  paralysis  the  study  of  the  field 
of  fixation  and  of  the  diplopia  are  the  two  essential  matters. 

Measurement  of  the  Field  of  Fixation. — This  is  useful 
not  only  for  the  assistance  which  it  renders  in  making  a 
diagnosis,  but  also  for  the  record  which  it  affords  as  to  the  degree 
of  paralysis.  It  enables  the  physician  to  know  whether  the  affec-* 
tion  is  improving  under  treatment.  The  field  of  fixation  is  de- 
termined with  the  tropometer  or  perimeter,  as  previously  de- 
scribed. 

Analysis  of  Diplopia. — The  existence  of  diplopia  is  demon- 
strated by  directing  the  patient  to  look  at  a  candle-light  or 
other  suitable  illumination,  placed  at  a  distance  of  three  meters 
or  more.  The  examination  should  be  conducted  in  a  darkened 
room,  and  preferably  against  a  black  background.  If  diplopia 
exists,  two  lights  will  be  seen.  The  image  which  is  well  defined 
(provided  the  visual  acuity  of  the  non-paralyzed  eye  is  good) 
and  correctly  projected  is  the  true  image,  while  the  indistinct  and 
incorrectly  localized  light  is  the  false  image.  By  covering  first 
one  and  then  the  other  eye  we  determine  which  eye  furnishes 
each  image ;  or  we  may  place  a  red  glass  before  one  eye,  thus 
coloring  the  light  as  seen  with  this  eye. 

After  the  existence  of  diplopia  has  been  determined,  the 
field  of  single  vision  and  the  field  of  diplopia  are  ascertained  by 
moving  the  light  in  various  directions,  while  the  patient  follows 
it  with  his  eyes,  his  head  remaining  unmoved ;  or,  as  recommended 
by  Landolt,  the  light  may  be  stationary,  while  the  patient's  head 
is  rotated  in  the  various  directions. 

In  making  the  diagnosis  of  the  seat  of  paralysis  the  main 
points  to  be  noted  are :  ( 1 )  Whether  the  false  image  is  seen  with 
the  right  or  with  the  left  eye;  (2)  whether  the  diplopia  is 
homonymous  or  crossed;  (3)  whether  the  two  images  are  parallel 
or  obliquely  inclined,  and,  if  inclined,  the  relative  direction  of  the 
false  image;  (4)  whether  the  two  images  are  on  a  level  or  one 


318  Disorders  of  Motility 

higher  than  the  other;  in  the  latter  case,  whether  the  true  or  the 
false  image  is  the  higher;  and  (5)  the  effect  of  varying  the  direc- 
tion of  the  gaze  upon  the  lateral  and  vertical  displacements  and 
upon  the  obliquity. 

By  careful  study  of  these  features  in  connection  with  the 
study  of  the  physiological  action  of  the  ocular  muscles  and  of 
the  result  of  their  paralysis,  as  delineated  in  the  foregoing  dia- 
grams, a  proper  diagnosis  may  usually  be  reached.  Simple  as 
this  procedure  may  seem,  die  diagnosis  of  oculo-muscular  paraly- 
sis is  in  many  cases  a  very  difficult  task.  This  is  because  the 
test  on  which  we  must  mainly  rely  (diplopia)  is  subjective ,  and 
even  intelligent  persons  are  very  liable  to  error  in  describing 
these  unfamiliar  visual  sensations.  In  the  examination  of  ignor- 
ant or  unobserving  patients  it  is  at  times  well-nigh  impossible  to 
gain  intelligible  answers.  The  most  difficult  cases  arc  those  of 
old  paralysis  and  of  paralysis  complicated  with  defective  visual 
acuity.  In  old  paralysis  and  that  in  which  the  acuity  of  the 
paralyzed  eye  is  defective,  diplopia  is  with  difficulty  evoked  and 
the  direction  of  projection  is  uncertain.  In  paralysis  complicated 
with  defective  acuity  of  the  non-paralyzed  eye  it  is  hard  to  dis- 
tinguish between  the  true  and  the  false  image. 

Measurement  of  the  Degree  of  Strabismus. — If  the  separa- 
tion between  the  diplopic  images  is  not  too  great,  fusion  may 
be  effected  by  the  interposition  of  a  prism  before  one  eye.  When 
the  prism  is  placed  before  the  paralyzed  eye  the  position  of  its 
base  must  correspond  with  the  direction  of  displacement  of  the 
false  image.  When  the  prism  is  placed  before  the  sound  eye  its 
base  must  be  in  the  opposite  direction.  It  is  impossible  to  rectify 
the  obliquity  of  the  false  image  with  a  prism,  but  when  the  two 
images  are  otherwise  brought  together  the  obliquity  is  usually 
overcome  either  by  rotation  of  the  head  or  with  the  aid  of  the 
sound  eye,  so  that  complete  fusion  of  the  images  results.  The 
strength  of  the  prism  required  for  fusion  measures  the  paralysis, 
each  prism-diopter  representing  about  one-half  of  a  degree  of 
strabismus.  For  the  purpose  of  record  the  measurements  should 
always  be  made  with  the  object  of  vision  in  the  same  direction. 

When  the  strabismus  is  too  great  for  prismatic  measurement, 
the  perimeter  may  be  used,  just  as  in  the  measurement  of  con- 
comitant strabismus. 

Still  another  method  consists  in  measuring,  on  an  opposite 


Paralytic  Disorders  of  Motility  319 

wall,  the  linear  distance  between  the  two  images;  the  distance  of 
the  patient  from  this  wall  being  known,  the  angle  of  strabismus 
may  be  deduced. 

Determination  of  the  Site  of  the  Lesion  Productive 
■of  Paralysis. — The  site  of  a  lesion  which  produces  paralysis 
is  to  be  conjectured  partly  from  the  apparent  etiology  and 
partly  from  the  accompanying  symptoms. 

Thus  paralysis  resulting  from  rheumatism,  diabetes,  lead- 
poisoning,  or  diphtheria  is  usually  peripheral  (orbital),  although 
all  except  the  first  of  these  diseases  is  known  to  be  capable  of 
producing  also  nuclear  paralysis.  Orbital  paralysis  may  also  be 
diagnosticated  when  there  are  definite  symptoms  pointing  to 
orbital  fracture,  hemorrhage,  inflammation,  or  tumor. 

Similarly,  in  paralysis  complicating  meningitis  a  basilar  lesion 
would  be  suspected.  Basilar  paralysis  may  also  be  caused  by 
hemorrhage,  tumor,  or  aneurism  compressing  the  ocular  nerves 
in  this  part  of  their  course.  A  basilar  lesion  would  be  especially 
indicated  by  symptoms  of  involvement  of  the  whole  group  of 
adjacent  nerves  of  one  side,  including  the  olfactory,  optic  and  the 
trigeminal,  in  addition  to  the  motor  nerves  of  the  eyeball. 

A  fascicular  lesion  is  determinable  only  in  crossed  paralysis, 
that  is,  when  the  paralysis  affects  the  third  or  sixth  nerve  of  one 
eye  with  simultaneous  hemiplegia  of  the  opposite  side.  The 
lesion  (hemorrhage  or  tumor)  must  in  this  case  lie  in  the  pyra- 
midal tract  (or  adjacent  to  it),  so  that  it  injures  the  nerve  fibers 
after  they  have  left  their  nucleus,  and  at  the  same  time  injures 
the  fibers  of  the  tract.  Since  the  latter  fibers  cross  to  the  oppo- 
site side  below  this  point,  the  hemiplegia  is  on  the  side  opposite 
to  the  affected  eye.  The  lesion  would  be  near  the  upper  or  lower 
border  of  the  pons,  according  as  the  third  or  the  .-,ixth  nerve 
were  involved.  The  seventh  (facial)  nerve  may  be  involved  in 
conjunction  with  the  sixth. 

A  nuclear  lesion  can  be  positively  diagnosticated  in  paralysis 
of  the  third  nerve  without  involvement  of  the  interna!  branches. 
A  peripheral  lesion  would  not  exclude  the  fibers  which  supply 
the  intrinsic  muscles,  but  owing  to  the  fact  that  the  nucleus  for 
the  latter  fibers  is  anterior  to  the  nucleus  for  the  rest  of  the  nerve, 
a  nuclear  lesion  may  not  implicate  the  internal  branch. 

It  does  not  follow,  however,  that  involvement  of  both  ex- 
ternal and  internal  muscles  is  necessarily  due  to  peripheral  dis- 


320  Disorders  of  Motility 

ease,  for  a  morbid  process  affecting  the  gray  matter  on  the  floor 
of  the  fourth  ventricle  may  evidently  attack  both  nuclei  of  the 
third  nerve.  It  may  also  attack  the  other  nuclei,  thus  causing 
paralysis  of  all  the  muscles  of  the  eye. 

Treatment. — Diphtheritic  paralysis  usually  undergoes  a 
spontaneous  cure,  which,  however,  should  be  assisted  by  tonic 
and  hygienic  measures. 

Rheumatic  paralysis  also  affords,  as  a  rule,  a  favorable  prog- 
nosis. The  treatment  consists  in  regulation  of  the  diet,  and  in  the 
administration  of  anti-rheumatic  remedies.  This  paralysis  is 
liable  to  recurrence  and  sometimes  proves  incurable. 

Diabetic  paralysis  is  favorably  influenced  and  sometimes 
cured  by  proper  regulation  of  the  diet.  In  lead  paralysis  a 
more  healthful  occupation  should  be  sought,  and  absorptives 
(iodides)  should  be  administered. 

In  orbital  paralysis  resulting  from  fracture,  sinusitis,  cellular 
inflammation,  exostosis,  tumor,  or  other  affection,  the  prognosis 
varies  in  accordance  with  the  extent  of  injury  inflicted  upon  the 
nerve  tissue.  The  treatment  consists  in  removing  the  causal' 
lesion,  as  far  as  this  may  be  possible. 

Paralysis  which  is  due  to  the  various  forms  of  poisoning 
(by  alcohol,  tobacco,  etc.)  affords  a  favorable  prognosis,  pro- 
vided the  deleterious  substance  is  eliminated  and  its  further  access 
prevented  before  destruction  of  the  nerve  tissue  ensues. 

Syphilitic  paralysis  is  usually  amenable  to  treatment  if  this 
is  undertaken  in  good  season ;  but  occasionally  this  form  of 
paralysis  resists  the  most  energetic  treatment,  destruction  of  tissue 
taking  place  before  absorption  of  the  pathological  deposit  can 
be  effected. 

Tabetic  paralysis  not  infrequently  disappears  with  the  ad- 
vance of  the  systemic  disease ;  but,  in  general,  paralyses  resulting 
from  incurable  brain  affections  present  an  unfavorable  prognosis, 
treatment  being  from  the  nature  of  the  case  unavailing. 

In  general  the  iodides  constitute  our  mainstay  in  the  treat- 
ment of  ocular  paralysis.  Strychnin  also  is  a  favorite  remedy, 
being  administered  usually  as  a  routine  procedure  in  those  cases 
"in  which  there  is  no  apparent  indication  for  the  use  of  the  iodides. 
Electricity,  which  was  formerly  much  used  in  the  treatment  of 
ocular  paralysis,  probably  has  no  beneficial  action  in  this  disease. 

Even  in  the  most   favorable  cases  paralysis  is  essentially  a. 


Paralytic  Disorders  of  Motility  321 

chronic  affection;  several  weeks  must  elapse — more  frequently 
two  or  more  months — before  a  cure  can  be  effected. 

Prismatic  Glasses. — In  slight  paresis,  the  separation  of  the 
images  not  being  great,  the  diplopia  may  be  avoided  by  the 
use  of  prisms.  Although  the  degree  of  paralytic  strabismus 
varies  with  the  direction  of  the  gaze,  so  that  it  is  not  possible  to 
order  a  prism  which  will  prove  satisfactory  throughout  the  field 
of  fixation,  yet  much  comfort  is  derived  from  a  prism  which  re- 
lieves the  diplopia  in  the  most  common  position  of  the  eyes — 
forward  and  slightly  downward.  In  paresis  of  one  of  the  de- 
pressor muscles,  the  superior  oblique  or  the  inferior  rectus,  it 
may  suffice  to  annul  the  vertical  displacement  by  a  prism  with  its 
base  down.  Unless  the  prism  is  very  weak  its  strength  should 
be  divided  between  the  two  eyes,  the  base  of  the  prism  before 
the  sound  eye  being  placed  upward.  If  both  vertical  and  lateral 
displacements  must  be  corrected,  the  base  of  the  prism  must  have 
an  intermediate  direction ;  or  the  vertical  error  may  be  corrected 
by  one  prism,  its  base  being  up  or  down,  while  the  lateral  error 
is  overcome  by  the  prism  before  the  other  eye,  its  base  being  in 
or  out,  as  required. 

It  is  not  necessary  to  overcome  the  entire  strabismus  by  the 
prismatic  action ;  when  a  certain  degree  of  assistance  is  rendered 
the  paretic  muscle,  the  latter  is  enabled  to  exert  its  remaining 
power  and  thus  to  produce  fusion  of  images.  On  this  account 
prisms  are  very  useful  in  paresis,  since  the  muscles  are  stimulated 
by  exercise,  and  contraction  of  the  antagonistic  muscles  is  pre- 
vented. The  strength  of  the  prismatic  correction  should  be  re- 
duced as  the  paresis  diminishes. 

Prismatic  and  Stereoscopic  Exercises. — Exercises  with 
prisms  or  with  the  stereoscope  are  also  advocated  in  paresis, 
and  may  be  found  useful  in  some  cases.  The  methods  are  the 
same  as  applied  in  concomitant  affections. 

Occlusion  of  the  Paralysed  Eye. — In  those  cases  in 
which  the  diplopia  cannot  be  overcome  by  prisms  suitable  for 
wearing  as  spectacles,  we  should  cover  the  affected  eye  with  an 
opaque  disk,  if  diplopia  causes  much  annoyance. 

Muscle  Stretching. — This  consists  in  grasping  the  eyeball 
with  forceps  and  rotating  it  forcibly  a  few  times  in  the  direc- 
tion of  action  of  the  paralyzed  muscle.  This  method,  applied 
for  one  or  two  minutes  every  day,  seems  to  exert  a  beneficial 


322  Disorders  of  Motility 

effect  in  some  cases,  chiefly  perhaps  by  preventing  contraction  of 
the  antagonistic  muscles.  It  is  not  advisable  in  recent  paralysis. 
A  local  anaesthetic  must  be  employed  to  prevent  pain. 

Operative  Treatment. — -This  is  permissible  only  in  old 
paralysis  in  which  there  is  decided  contraction  of  the  principal 
opposing  muscle,  and  in  which  there  is  no  hope  of  curing  the 
paralysis.  The  frequency  of  indication  for  such  treatment  is 
diminished  by  the  fact  that  in  long-continued  paralysis  annoying 
subjective  disturbances  are  usually  absent.  In  those  cases  in 
which  operation  is  apparently  indicated  the  result  is  frequently 
disappointing.  The  most  that  can  be  expected  is  improvement  of 
the  strabismus  and  relief  from  diplopia  in  the  more  common. direc- 
tions of  the  eyes.  Operation  can  be  of  no  benefit  unless  there  is 
some  power  left  in  the  affected  muscle.  Advancement  of  the 
muscle  may  increase  this  power,  but  if  the  antagonistic  contrac- 
tion is  very  great,  tenotomy  of  the  latter  muscle  must  be  com- 
bined with  the  advancement  of  the  paralyzed  muscle.  In  paraly- 
sis of  the  superior  oblique,  as  well  as  in  that  of  the  inferior 
rectus  advancement  of  the  latter  muscle  is  the  operation  to  be 
selected. 

Paralyses  of  Associated  Movements 

A  lesion  situated  above  the  nerve-nucleus  cannot  produce  a 
monocular  disturbance  of  motility.  Any  limitation  of  movement 
produced  by  a  lesion  so  situated  must  be  binocular.  This  limita- 
tion may  consist  in  inability  to  turn  the  two  eyes  consensually  to 
the  right  or  to  the  left,  or  upward  or  downward ;  or  all  these 
motions  may  be  normally  performed,  and  yet  the  power  of  simul- 
taneously contracting  the  two  internal  recti  for  convergence  may 
be  totally  lacking. 

Conjugate  lateral  deviation  of  both  eyes  to  the  right  or  left 
not  infrequently  occurs  as  a  transitory  symptom  in  cerebral 
hemorrhage.  The  cortical  center  for  rotation  of  the  two  eyes  to 
the  right  lies  in  the  left  hemisphere.  Hence  ^  destructive  lesion 
in  the  left  hemisphere  causes  a  loss  of  power  of  deviation  to  the 
right,  with  consequent  deviation  of  the  eyes  to  the  left;  that  is, 
the  eyes  look  towards  the  lesion.  This  is  just  the  opposite  to 
what  occurs  in  irritative  lesions,  such  as  give  rise  to  epileptiform 


Paralytic  Disorders  of  Motility  323 

convulsions.  The  spasmodic  deviation  produced  by  an  irritative 
lesion  may  at  any  time  be  replaced  by  paralysis,  if  the  lesion  is 
of  sufficient  magnitude  to  produce  destruction  of  tissue. 

Conjugate  deviation  occurring  in  apoplectic  attacks  is  a 
distant  symptom — that  is,  the  centers  of  ocular  motion  are  not 
injured.  The  deviation  probably  results  from  suspension  of 
function  in  the  entire  hemisphere  (Stvansy).  There  being  no 
stimulation  of  the  affected  side,  the  opposing  muscles  draw  the 
eyes  in  the  opposite  direction.  The  function  of  the  affected 
hemisphere  may  be  restored,  or  if  permanently  injured  the  other 
hemisphere,  through  intimate  association,  comes  to  the  rescue, 
and  the  deviation  is  overcome. 

Although  conjugate  lateral  deviation  is  known  to  result  from 
a  lesion  situated  in  the  cortex  or  in  the  optic  radiations,  it  can 
not  be  said  that  all  associated  paralyses  are  due  to  lesions  in  this 
region.  We  do  not  know  the  situation  of  the  lowest  centers  or 
nuclei  which  preside  over  binocular  action.  It  appears  from  the 
result  of  autopsies  that  in  the  case  of  lateral  movements  a  portion 
of  the  nucleus  of  the  sixth  nerve  exercises  this  control,  since 
fibers  from  this  nucleus  pass  to  the  opposite  internal  rectus  as 
well  as  to  the  external  rectus  of  its  own  side.  Thus  it  would  seem 
that  the  nucleus  of  the  sixth  nerve  on  either  side  controls  lateral 
movement  to  the  corresponding  side.  Hence  destruction  of  the 
nucleus  at  the  point  of  origin  of  these  two  sets  of  fibers  causes 
conjugate  lateral  paralysis.  This  symptom — conjugate  lateral 
paralysis — is  also  sometimes  produced  by  pressure  upon  the 
nerves  by  a  lesion  in  the  pons.  In  all  these  cases  the  deviation 
is  opposite  to  that  which  occurs  in  cortical  lesions ;  that  is,  the 
eyes  look  away  from  the  lesion. 

Paralysis  of  upward  or  downward  movements  of  both  eyes 
generally  results  from  pressure  by  a  tumor  in  the  quadrigeminal 
region. 

Paralysis  of  Convergence. — This  may  be  complete  or 
partial ;  in  the  latter  case  it  resembles  non-paralytic  insufficiency 
of  convergence,  and  in  some  cases  a  distinction  may  be  impos- 
sible. 

Complete  paralysis  of  convergence  consists  in  a  total  aboli- 
tion of  the  converging  power  without  loss,  as  a  rule,  of  power  in 
any  of  the  individual  muscles,  although  the  latter  may  be  impli- 
cated by  extension  of  the  morbid  process.     Accommodation,  on 


324  Disorders  of  Motility 

the  other  hand,  usually  participates  in  the  paralysis,  but  without 
mydriasis.  The  eyes  assume  a  position  of  parallelism  or  slight 
divergence,  maintaining  this  position  in  near  vision  with  resulting 
crossed  diplopia. 

The  nucleus  for  convergence  probably  lies  in  the  aqueduct 
of  Sylvius,  near  the  nuclei  for  the  ciliary  muscles.  Hence  in 
paralysis  of  convergence  a  lesion  in  this  region  is  presupposed,  as 
it  is  unlikely  that  a  cortical  lesion  would  produce  this  paralysis 
without  giving  rise  to  other  and  graver  symptoms. 

In  the  etiology  of  paralysis  of  convergence  tabes  holds  the 
first  place,  this  being  the  cause  in  the  majority  of  cases  which 
have  been  observed.  Other  causes  are  syphilis  and  poisoning  by 
alcohol  and  tobacco. 

Paralysis  of  Divergence. — This  sometimes  occurs  in 
conjunction  with  paralysis  of  convergence,  as  manifested  by 
homonymous  diplopia  in  distant  vision,  together  with  crossed 
diplopia  in  near  vision.  Paralysis  of  divergence  may  also  occur 
without  paralysis  of  convergence,  the  etiology  being  the  same  as 
in  the  latter  affection. 

Treatment  of  Paralysis  of  Associated  Movements. — 

This  is  such  as  is  appropriate  for  the  causal  lesion,  so  far  as 
that  admits  of  cure.  In  paresis  of  convergence  or  of  divergence 
the  enfeebled  action  may  be  assisted  by  the  use  of  prismatic 
glasses  within  the  limits  to  which  such  glasses  are  subject. 

The  following  authorities  have  been  consulted  in  the  prep- 
aration of  the  foregoing  chapter: 

Stevens,  Motor  Apparatus  of  the  Byes. 
Howe,  Muscles  of  the  Byes. 
Maddox,  Ocular  Muscles. 

Duane,  Bxtra-Ocular  Muscles,  Posey  and  Spiller's  Eye  and 
Nervous  System. 

Fuchs,  Text  Book  of  Ophthalmology. 

Landolt,  Anomalies  of  the  Motor  Apparatus  of  the  Byes, 
Norris  and  Oliver's  System  of  Diseases  of  the  Eye. 

Evans,  Congenital  Defect  of  Abduction  zinth  Retraction  of 
the  Byeball  in  Adduction,  Ophthal.  Review,  1903. 


Paralytic  Disorders  of  Motility  325 

Swanzy,  Eye  Diseases  and  Bye  Symptoms  in  their  Relation 
to  Organic  Diseases  of  the  Brain  and  Spinal  Cord,  Norris  and 
Oliver's  System  of  Diseases  of  the  Eye. 

Posey,  Congenital  Squint,  Trans.  Am.  Ophth.  Soc,  1907; 
and  Paralysis  of  the  Upward  Movements  of  the  Byes,  Report 
Sec.  on  Ophth.,  College  of  Phys.  of  Phila.,  1903. 


APPENDIX 


ALGEBRAIC  FORMULAE 

In  order  that  we  may  have  a  proper  knowledge  of  the  various 
optical  problems  which  are  presented  in  ophthalmology  we  must 
study  the  elementary  algebraic  formulas  by  which  we  trace  the 
path  of  refracted  rays  of  light. 

Deviation  Effected  by  a  Prism 

In  Fig.  141  B  A  C  represents  a  section  in  the  principal 
plane  of  a  prism,  of  which  A  (a)  is  the  refracting  angle.  The 
line  0  S  S1  R  is  a  ray  passing  through  the  prism  in  its  principal 


fig.  141 

plane;  N  M  is  the  normal  at  the  point  of  incidence,  and  Nt  M 
is  the  normal  at  the  point  of  emergence  of  the  ray. 

The  reader  who  has  even  an  elementary  knowledge  of 
geometry  will  readily  understand  the  following  equations : 

S,  M  P  =  a 

[The  angle  formed  by  the  intersection  of  two  lines  is  equal 
to  the  angle  formed  by  the  intersection  of  two  other  lines  per- 
pendicular to  the  first  two  lines.] 

S1  M  P .=  r  +  r' 

[The  sum  of  two  angles  of  a  triangle  is  equal  to  1800  less 
the  third  angle.] 

Therefore  r  +  r'  =  a 

The  deviation  of  the  ray  at  the  first  refraction  is  evidently 
equal  to  the  difference  between  the  angles  of  incidence  and  re- 

32« 


Appendix  $2j 

fraction  (i  —  r),  and  the  deviation  at  the  second  surface  is  simi- 
larly expressed  by  e  —  r'.  The  total  deviation  is  expressed  in 
the  equation : 

D  =  i  —  r  +  e  —  r', 
or,  since  r  -\-  r'  =  a, 

D  =  i  -f-  e  —  a 

From  this  equation  we  see  that  the  deviation  effected  by  a 
prism  is  equal  to  the  sum  of  the  angles  of  incidence  and 
emergence,  less  the  refracting  angle  of  the  prism. 

For  the  symmetrical  ray— the  ray  of  minimum  deviation—? 

a 
is.  equal  to  e,  r  is  equal  to  r' ,  and,. consequently,  r  ==    .    ■ 

From  this  equation  and  from  the  equation  for  refraction, 
sin  i  =  n  sin  r,  we  can  replace  r  by  its  equivalent  in  terms  of 
the  refracting  angle,  a: 

.      a  * 

sin  i  =  n  sin 

2 

If  we  know  the  refractive  index  (m)  and  the  refracting  angle 
(a),  we  can  ascertain  the  value  of  i  from  a  table  of  sines.  The 
minimum  deviation  is  then  determined  from  the  equation 

D  =  2i  —  a 


For  the   ray  of  perpendicular   incidence   i  and   r  are   each 
zero;  therefore,  r'  =  a 
and  D  =  e  —  a 

If  we  know  the  index  and  the  refracting  angle  we  can 
determine  e  from  the  equation 

sin  e  —  n  sin  r'  =  n  sin  a 

We  thus  find  the  value  of  e  from  a  table  of  sines  and  sub- 
stitute this  value  in  the  equation 

D  =  e  —  a 

In  this  way  the  table  (p.  30)  has  been  constructed,  giving 
the   deviation   effected  by  prisms   of  various   refracting  angles. 

In  constructing  the  table  showing  the  deviation  of  prisms 
in  terms  of  the  prism  diopter  it  is  only  necessary  to  take  from 
a  table  of  tangents  the  angle  which  corresponds  to  the  tangent, 
as  this  is  represented  by  the  number  of  the  prism.  Thus  the  de- 
viation effected  by  a  prism  of  1  A  is  the  angle  whose  tangent  is 
1,  and  so  on. 

•If  these  angles  are  small  we  may  replace  the  ratio  of  their  sines  i « y  iliaio:'  the  angles 
themselves,  and  if  »■=  1.5  (the  approximate  index  forglass),  sin  (  =  »  sin  —  heoomes  i  ■■-  —   it, 

and  I)  =  — .     That  is,  for  prisms  of  small  refracting  angle  the   deviation    is   ariout   one-half 
of  this  angle. 


328  Appendix 

Relation   between   Conjugate   Points   in    Refraction   at   a 

Spherical  Surface 

In  deriving  the  algebraic  equation  between  conjugate  points 
in  refraction  at  a  spherical  surface  we  take  the  condition  shown 
in  Fig.  142,  as  the  typical  case  because  it  is  convenient  for  us  to 
regard  the  terms  as  positive  when  the  surface  is  convex,  and 
when  the  rays  proceed  from  a  real  focus  (O)  and  converge 
after  refraction  to  a  real  focus  (/). 

The  straight  line  0  I  (the  unrefracted  ray)  which  passes 
through  the  center  of  the  surface  is  the  axis.  All  distances  are 
measured  on  this  line. 

In  the  diagram  S  A  S  represents  a  section  of  the  convex 
refracting  surface,  and  S  Bx  S  represents  the  wave  front  as  it 


would  be  at  a  certain  time  if  the  retarding  medium  were  absent; 
but  owing  to  this  retarding  medium  the  actual  wave  front  at 
this  time  is  S  B  S.  While  the  wave  would  have  advanced  from 
A  to  Bx,  in  the  rarer  medium,  it  is  so  retarded  by  the  dense 
medium  that  it  advances  only  as  far  as  B.  These  distances  are 
inversely  proportional  to  the  velocity  of  light  in  the  two  media. 
If  therefore  n  represents  the  refractive  index  of  the  first  and  nx 
that  of  the  second  medium,  it  is  apparent  that 

n  X  A  Bx  =  Wl  X  A  B 

It  also  appears  from  the  diagram  that 

AB  =  AD  —  BD 
and  that 

A  Bx  =  A  D  +  D  Bx 
and  therefore 

n  (A  B  +  D  Bx)  —  nx  (A  D  —  D  B) 


or, 


n  X  D  Bx  +  nx  D  B  =  (nx  —  n)  A  D     .     .     .     (a) 


The  distances  D  Bx,  D  B  and  A  D  are  not  practically  meas- 
urable, but  they  express  respectively  the  curvature  of  the  incident 
wave,  of  the  refracted  wave  and  of  the  refracting  surface. 

If  the  arc  S  Bx  S  \s>  infinitesimal,  the  bending  or  curvature 
of  this  arc   is  measured  by  the  perpendicular  distance  D  Bx. 


Appendix  329 

Similarly,  under  the  same  conditions  the  curvatures  of  the  arcs 
S  B  S  and  S  A  S  are  measured  by  D  B  and  A  D  respectively. 

As  the  size  of  the  arc  increases  the  perpendicular  distance 
cannot  be  taken  as  the  exact  measurement  of  the  curvature,  but 
for  the  small  pencils  of  light,  such  as  enter  the  pupil  of  the  eye, 
the  error  arising  from  these  measurements  is  negligible. 

But  there  are  other  and  more  convenient  measurements 
which  express  the  curvatures  of  the  waves  and  of  the  surface — 
the  reciprocals  of  their  radii  of  curvature.     Thus  the  curvature 

of  the  incident  wave  is  expressed  by-^-^.;  the  curvature  of  the 
refracted  wave  is  expressed  by  -j~  ;  and  the  curvature  of  the 

refracting  surface  by        ,  r  being  the  radius  of  this  surface. 

Hence,  these  expressions  could  be  substituted  in  equation  (a) 
for  D  Blt  D  B  and  A  D,  respectively;  but  here  still  another 
substitution  must  be  made  which  is  only  approximately  correct. 
It  must  be  borne  in  mind  that  the  distances  O  A,  O  S,  I  S  and  I A 
are  all  very  great  in  proportion  to  the  arc  S  A  S,  and  that  con- 
sequently in  actual  measurement  there  would  be  very  little  dif- 
ference between  O  S  and  O  A,  and  between  /  5*  and  /  A*.  These 
distances,  O  A  and  /  A,  measured  on  the  axis,  may,  therefore, 
be  substituted  for  O  S  and  /  S,  respectively,  and  consequently 
for  D  Bx  and  D  B  in  equation  (a),  which,  therefore  becomes 

n  7i\  (tii  —  n) 

A~0  +  ~Al  =         r~ 

or  by  substituting  /  and  /'  for  O  A  and  A  I,  respectively, 

This  equation,  expressing  the  relation  between  conjugate 
focal  distances  (/  and  /')  is,  as  has  been  shown,  only  approxi- 
mately correct.  It  is,  however,  sufficiently  so  for  the  purposes 
of  ophthalmological  study,  although  it  would  be  far  from  suffi- 
cient for  the  construction  of  microscopes  or  other  instruments  in 
which  spherical  aberration  could  not  be  neglected. 

Within  these  prescribed  limits  this  equation  is  applicable  for 
all  cases  of  refraction  at  a  spherical  surface. 

When  nx  is  greater  than  n,  and  r  is  positive,  the  refraction 
takes  place  in  the  passage  of  the  wave  from  a  rarer  to  a  denser 
medium  at  a  convex  surface ;  when  n1  is  less  than  n  and  r  posi- 
tive, the  refraction  is  that  of  a  wave  passing  from  a  denser  to 


*The  proper  proportious  can  not  be  represented  diagnimmaticailjr. 


330  Appendix 

a  rarer  medium  at  a  convex  surface;  when  r  is  negative,  the  re- 
fracting surface  is  concave;  and  when  r  is  infinite  the  surface 
is  plane. 

Principal  Foci  and  Focal  Distances. — When  O  is  so 
far  distant  from  the  surface  that  the  wave  may  be  regarded 
as  plane  and  the  rays  as  parallel,  the  distance  A  O  (/)  must  be 

regarded   as   infinite,   and   consequently  —  is   zero.      By   making 

this  substitution  in  equation  ( I )  we  derive  for  the  correspond- 
ing value  of  /'  the  equation  ,  ij 

s>    __       »i  r 

J      — ■   ,. 


;/,   —    ?i 


This  equation  determines  the  focusing  point  for  rays  that 
are  parallel  before  refraction.  The  distance  (A  F')  of  this 
point  from  the  surface  is  the  posterior  (or  second)  principal 
focal  distance;  it  is  denoted  by  the  letter'/7',  the  value  of  F' 
being  derived  from  the  equation 

\  '•  ,-•■•  i 

buy,  /•"'  Ux  }     . 

n1  — n 

The  point ,. at  which  parallel  rays  are  focused,  as  .determined 
by  this  equation,  is  called  the  posterior  (or  second)  principal 
focus  (F'). 

Similarly,  if  /'  is  infinite  in  equation  (i),  we  have  : 

/;      »r 


»!  —   n 


;    '  ■    ■   '  ■     ■  . 

This  equation  determines  the  point  of  origin  of  rays  which 
become  parallel  after  refraction.  The  distance  A  F  is  the 
anterior  (or  first)  principal  focal  distance;  it  is  denoted  by  the 
letter  F.  The  point  (F)  from  which  rays  must  diverge  in  .order 
that  they  may  be  parallel  after  refraction  is,  the  anterior  (or  first ) 
principal  focus.     Since 

„  n  r     '■  ;/,    r 

r  =  -  — ,  and  /*'  ■===■  — - 


nx   —    )i  ux  —  ;/ 


equation   (i)   becomes 


+    4f    =      I     ^^r-         (a) 


/  /'  F  F'  * 

Equation  (2)  may  also  be  written  in  the  form 

'  '    ;  F       ,      F' 

f  +  r  =  l      iy) 


Appendix 


33* 


When   the   index   of   the   first  medium   is  unity,   as  in   air, 
equation  (2)  becomes 

1  n  1 


/ 


/' 


F 


If  /  represents  the  distance  of  any  conjugate  focus  from  the 
anterior  principal  focus,  and  /'  the  distance  of  the  corresponding: 
posterior  conjugate  from, the  posterior  principal  focus,  /  is  equal 
to  /  +  F,  and  /'  is  equal  to  I'  -f  F' '■ 

By  substituting  these  values  for  /  and  /'  in  any  of  the  fore- 
going equations  we  derive  the  equation 

W  =  F  F'      (4) 

Equations  (/),  (2),  (3)  and  (4)  constitute  all  of  the  com- 
monly used  equations  expressing  the  relation  between  conjugate 
points,  but  there  remains  one  other  form  of  this  relation  which 
will  be  required  in  the  investigation  of  the  refraction  by  the 
several  surfaces  of  the  eye. 

For  the  derivation  of  this  equation  we  use  Fig.  143.  BxO  A\ 
represents  a  half  section  of  the  incident  pencil,  while  Bx  I  Ai 


a 

r1— — — Js 

\h 

180-aT  T---- 

— -f» 

At 

m a, 

I 

FIG.    143 

represents  the  corresponding  refracted  pencil.  The  angle  B1  0  Ax 
(a)  represents  the  divergence  of  the  incident  pencil,  while  the  con- 
vergence of  the  refracted  pencil  is  represented  by  Bx  I  At  (180 

The  perpendicular  Bx  Ax   (which  we  call  b)  represents  the 
principal  plane.     Then 

f(OAY)  =       *        and/' "K   /) 


tan  a 
or  /' 


tan  (180  —  a,) 


h 

tan   a, 


By  substituting  these  values  for  /  and  /'  in  equation  (3)  we 
derive 

n  tan  a  ni  tan  a,  n 

b  b  F 


(5) 


We  also  make  use  of  the  relation  between  the  angles  of 
divergence  of  the  incident  and  refracted  pencils  in  comparing 
the  size  of  the 'object  and  its  image.     If  we  express  the  relative 


332  Appendix 

size  of  the  object  and  its  image  by  means  of  their  respective 
distances  from  the  nodal  point,  we  have  the  equation 

-=£±^       (6)* 

From  equation  (i)  we  derive  the  value  of  r  in  terms  of  n,  it,, 
/  and  /' 


(r  _  (»i -»).//'\ 


<?        »j/ 

*        »/'• 

,  we  have  — - 
z 

=  — 

nx  tan  ax 

?i  tan   a 

and  substitute  this  value  in  (6)  ;  whence  by  reduction  we  derive 


But  since 

/'  tan  a 

f  tan  ax 

Since  the  image  in  one  refraction  may  become  the  object  in  a 
successive  refraction,  we  may  express  the  relation  between  an 
object  and  its  successive  images  by  the  following  equation: 

—  o .  n .  tan  a  =  ix.  nx.  tan  ax  =  i2.  n2.  tan  a2  =  iz.  n3.  tan  a3  = 

i4.  w4.  tan  a4, 

and  so  on  for  any  number  of  refractions.f  If  after  the  last  re- 
fraction the  image  is  of  the  same  size  as  the  original  object  and 
on  the  same  side  of  the  axis  we  have  the  equation 

n  .  tan  a  —  «4  tan  a4  (7) 

This  equation  is  used  for  determining  the  principal  points 
of  a  compound  optical  system. 

Relation  between  Conjugate  Points  in  Refraction  by 

Lenses 

Refraction  by  a  biconvex  lens  is  illustrated  in  Fig.  144,  in 
which  a  wave  diverging  from  0  is  represented  as  converging 
to  /-i  as  the  result  of  refraction  at  the  first  surface  of  the  lens, 
and  as  the  result  of  the  second  refraction  the  wave  which  is 
converging  to  Ix  is  rendered  more  convergent  and  is  focused  at  I2. 

This  is  only  one  of  several  conditions  that  may  obtain ;  the 
wave  may  remain  divergent  after  the  first  refraction,  being  ren- 
dered convergent  by  the  second  refraction  (illustrated  by  revers- 

*  Page  43. 

tThe  first  term  of  this  equation  is  negative  because  the  object  ii  inverted  with  respect  to 
the  image  ;  in  the  subsequent  terms  the  positive  signs  indicate  that  the  object  and  image  lie  on 
the  same  side  of  the  optic  axis. 


Appendix  333 

ing  the  course  of  the  rays  in  the  diagram)  ;  the  wave  may  remain 
divergent  or  it  may  be  plane  after  the  two  refractions;  it  may 
be  plane  or  convergent  before  refraction,  its  convergence  being 
increased  by  the  refraction. 

The  condition  of  a  diverging  pencil,  brought  to  a  real  focus 
by  the  two  combined  refractions,  as  illustrated,  is  taken  as  a 


^-/( 


FIG.    144 

typical  case  for  the  derivation  of  the  formula,  because  it  is  more 
convenient  for  us  to  regard  the  focal  distances  as  positive  when 
the  foci  are  real,  as  in  the  diagram. 

Applying  formula  (1)  to  the  first  refraction,  we  derive  the 
equation 

1  ?i  71  —  1  1 


ON     '     NIX  r  F; 

in  which  w,  the  refractive  index  of  the  lens,  is  greater  than  that 
of  the  surrounding  air;  r  is  the  radius  of  curvature  and  Fx  is 
the  distance  (N  Fx)  of  the  lens  from  the  principal  focus  Fx  of 
this  refraction. 

Applying  formula  (1)  to  the  second  refraction  and  remem- 
bering that  as  regards  this  refraction  N  Ix  is  negative,  as  is 
also  rlt  the  radius  of  the  surface,  we  derive 

n  1  1  --n  n  —  1  1 


NIX      '     NI2  —  rx  r,  F2' 

F2  being  the  distance  (N  F2)  from  the  lens  to  the  principal  focus 
F2  of  the  second  refraction. 

Adding  these  two  equations  and  replacing  0  N  and  iV  I2  by 
/  and  /',  respectively,  we  derive 


f,  =  («-•)  (-  +    r)   =  F-  +  jr-     (8) 


I 

/  / 


If  we  make  /  infinite  in  the  above  equation,  we  derive 

F,  +  F* 

as  the  corresponding  value  for  the  second  principal  focal  dis- 
tance, and  if  we  make  /'  infinite,  we  derive  this  same  value  for 
the  first  principal  focal  distance.    Hence,  in  a  lens  the  two  princi- 


334 


Appendix 


pal  focal  distances  are  equal  and  (in  thin  lenses)  the  reciprocal 
of  this  distance  (  „  )  is  equal  to  the  sum  of  the  reciprocals  of 
the  principal  focal  distances 

of  the  two  separate  refractions. 

If  we  make  this  substitution,  equation  (8)  becomes 


/ 


+ 


i 

7' 


i 

F 


(9) 


which    is   the    form    in   which   the   equation   between   conjugate 
points  for  lens  refraction  is  usually  written. 

If  either  r  or  rt  is  infinite,  that  is,  if  one  surface  of  the 
lens  is  plane  and  the  other  convex,  equation  (8)  becomes 


i 

7 


i 
/' 


;/  —  i 
r 


(io) 


By  the  appropriate  modification  of  the  signs  of  r  and  rx  we 
can  apply  the  foregoing  equations  to  plano-concave,  convexo- 
concave  and  biconcave  lenses. 

But  when  the  thickness  of  a  lens  is  appreciable  as  compared 
with  its  focal  length  these  equations  are  not  applicable,  since 
the  distance  between  the  two  surfaces  has  been  disregarded  in 
the  derivation  of  the  formulae.  A  thick  lens  constitutes  a  com- 
pound optical  system  and  its  cardinal  points  are  determined  by 
the  method  next  to  be  given  for  such  a  system. 

The  Cardinal  Points  of  the  Schematic  Eye 

Listing  in  deducing  his  schematic  eye  used  the  method  of 
Gauss,  in  which  the  path  of  any  refracted  ray  is  determined  by 
means   of  analytical  geometry.      Helmholtz  adopted   a  different 


T 
\ 


fig.   145 


method.  He  determined  first  the  cardinal  points  of  the  corneal 
refraction,  then  the  cardinal  points  of  the  crystalline  lens  and 
combined  these  two  systems,  determining  thereby  the  cardinal 
points  of  the  combination.     The  process  is  necessarily  tedious, 


Appendix  335 

whatever  method  is  used,  but  that  which  I  here  give  has  the 
advantage  that  the  diagrammatic  illustration  is  easily  understood 
and  that  only  an  elementary  knowledge  of  mathematics  is  de- 
manded. 

The  refractions  which  occur  at  the  several  surfaces  of  the 
eye  are  illustrated  in  Fig.  145. 

Applying  equation  (5)  to  the  first  refraction  (at  the  an- 
terior surface  of  the  cornea)  we  have 

tan    a  n,  tan  a.  I 

K     "  '      >,       =  K     <5a) 

Applying  equation  (5)  to  the  second  refraction  (at  the  pos- 
terior surface  of  the  cornea)  we  have 

;/.  tan  a,  >i .,  tan  a.,  n ,         ,   ,  . 

K      ~      K      =  f:    (5b) 

In  the  third  refraction  (at  the  anterior  surface  of  the  crystal- 
line lens  )  we  have 


n 2  tan  a3  >i s  tan  as  nt 


b,  b^  /■: 


1 


And  in  the  fourth  refraction, 


;/.,  tan  a  .  n  ,  tan  a  ,  ;/ . 


(so 


(5d) 


It  appears  also  from  Fig.  144 

that  [A2B2]  b2=  [Ax  Bx]  b1—A1A2tan(j8o^ai1). 
Similarly 

bs  =  b2  —  A2  A3  tan  (180  —  a2) 
and 

&4  =  bs  —  A3  A±  tan  (180  —  a3) 

Replacing  the  tangent  of  1800  minus  the  angle  by  minus  the 
tangent  of  the  angle,  and  writing  tlt  t2  and  t3  for  the  intervals 
between  the  surfaces,  we  have  the  following  equations : 

b2  ==.  bx  -f-  tx  tan  ax  (na) 
b3  =  b2  -j-  t2  tan  a2  (11b) 
b4  =  b3  -j-  h  tan  a3  (nc) 
and  also 

bx  =  f .  tan  a 

By  making  the  proper  substitutions  in  these  two  sets  of 
equations  we  can  eliminate  the  intermediate  terms  and  derive  a 
relation  between  any  point  and  its  conjugate  after  the  four  re- 
fractions, but  as  our  desire  is  only  to  apply  this  process  to  the 


336  Appendix 

eye,  not  to  deduce  the  general  algebraic  formula,  which  is  com- 
plicated, we  proceed  at  once  with  the  arithmetical  substitutions. 
The  following  table  gives  the  values  which  may  be  accepted 
as  average  measurements  of  the  normal  human  eye. 

RADII    OF    CURVATURE 

Anterior  surface  of  the  cornea 7.8  mm.  (rj 

Posterior  surface  of  the  cornea 6    mm.  (r2) 

Anterior  surface  of  the  lens 10    mm.  (r3) 

Posterior  surface  of  the  lens 6     mm.  (r4) 

INDICES  THICKNESSES 

Cornea 1.377  (ni)  1     mm.  (tj 

Aqueous  humor. .  .  1.337  ("2)  2.6  mm.  (t2) 

Lens 1.437  (n3)  4    mm.  (t3) 

Vitreous  body.  . . .  1.337  (n4) 

By  numerical  substitution  we  derive  the  following  values : 
■p-  =  — =  0.0484  ;      ^  =  -5 i  =  —  0.0066  ; 

» .  _  _3 s  =  0.01  ;         -= 3- =  -* s- =         o.or68; 

-J-  =  0.7262  ;         -A-  =  1.9446  ;         -J-  =  2.7816. 

n\  7l2  n3 

Placing  the  value  of         here  obtained  in  equation  (5  a)  and 

■**  1 
assigning  to  ^  (1.377),  its  value,  we  derive 

tan  ax  =  —  -0331  bx  -f-  .7262  tan  a 

We  now  place  this  equivalent  for  tan  ax  in  equation  (n  a)  and 
substitute  for  tj  its  value.    The  result  is 

b2  =  .9649  b1  -+-  .7262  tan  a 

We  next  proceed  to  the  second  refraction  and  substitute  this  value 

71 

of  b2  and  also  the  value  found  for  tan  ax  and  for  ^=-  in  equation 

(5  b),  as  follows: 

—  .0484  bx  -(-  tan  a  —  n2  tan  a2  =  —  .0066  (.9649  bx  -f- 

.7262  tan  a) 
whence  by  reduction 

+  n2  tan  a2  =  —  .0421  bx  -f-  1.0048  tan  a. 


Appendix  337 

Similarly  in  the  third  refraction  we  have 

—  .0421  b1  -f-  1.0048  tan  a  —  n3  tan  a3  =  .01  b3. 
and 

b3  =  .9640  bx  -f-  .7262  tan  a  -\-  1-9466  ( —  .0421  bx  -f- 

1.0048  tan  a) 
or 

b3  =  .8831  bx  -\-  2.6801  tan  a 
Therefore 

—  .0421  bx  -\-  1.0048  tan  a  —  n3  tan  a3  = 

.0088  bx  -\-  .0268  tan  a 
or 

n3  tan  a3  =  —  .051  bx  -\-  .978  tan  a. 

In  the  fourth  and  last  refraction  we  have 

b4  =  .8831  bx  -J-  2.6801  tan  a  +  2.7816  ( —  .051  bx  -j-  .978  tan  a) 

or 

b*  —  •74I5  K  +  5-4005  tan  a  (12) 

Substituting  this  value  of  b4  and  the  values  found  for  n3  tan  a3 

n 
and  for     3  in  equation  (5d),  we  derive 

—  .057  bx  -f-  .978  tan  a  —  w4  tan  a4  =  . 0168  (.7415  bx  + 

5.4005  tan  a) 
and  by  reduction, 

—  n4  tan  a4  =  .0634  bx  —  -8873  tan  a 
If  by  is  replaced  by  its  equivalent  /  tan  a,  this  equation  becomes 

—  n4  tan  a4  =  .0634  f  tan  a  —  -8873  tan  a  (13) 

in  which  /  is  the  distance  of  the  anterior  conjugate  point  from 
the  anterior  surface  of  the  cornea  and  tan  a  and  tan  a4  are  the 
tangents  of  the  angles  which  any  ray  from  this  point  makes  with 
the  optic  axis  before  and  after  refraction  by  the  four  surfaces 
of  the  eye. 

From  equations  (12)  and  (13)  we  can  determine  all  the 
cardinal  points  of  the  eye. 

Anterior  Principal  Focus. — For  finding  the  position  of 
this  point  we  use  equation  (13).  Since  rays  proceeding  from 
the  anterior  focus  are  parallel  to  the  optic  axis  after  refraction, 
a4  becomes  zero  (or  1800)  and  tan  a4  =0,  and  if  we  divide  by 
tan  a  the  equation  becomes 

.0634  f  =  .8873 
or 

/  =  13-99 

The  distance  of  the  anterior  focus  from  the  anterior  surface  of 
the  cornea  is  therefore  13.99  mm- 


338  Appendix 

Posterior  Principal  Focus. — For  finding  the  position  of 

this  point  we  use  equations  (12)  and  (13).  Since  rays  which 
meet  at  the  posterior  focus  are  parallel  to  the  optic  axis  before 
refraction,  a  is  for  this  point  zero  (or  1800)  and  tan  a  =  0. 
Equation  (12)  therefore  becomes 

K  =  -7415  K 

Also  when  tan  a  =  o  equation  (13)  becomes  (writing  bx  for 
f  tan  a) 

—  nt  tan  a4  =  .0634  &i 
and,  since 

tan  (180  —  a4)  =   —  tan  a4  =  -.*,     "^  =  .0634  <*r 

Substituting  for  bA  its  value  .7415  blt  as  above  deduced,  we  have 

1-337  X    .7415   *i  ,A  , 

=  .0634  £,, 

and  by  reduction 

U  =  15.62 

The  distance  of  the  posterior  focus  from  the  posterior  sur- 
face of  the  crystalline  lens  is  therefore  15.62  mm,  and  since 
this  surface  lies  7.6  mm  behind  the  anterior  surface  of  the 
cornea,  the  posterior  focus  lies  23.22  mm  behind  the  latter  surface. 

First  Principal  Point. — We  determine  the  position  of  this 
point  from  equation  (13).  We  recall  that  the  two  principal 
points  are  conjugate  points  such  that  a  ray  directed  towards  a 
point  in  one  principal  plane  appears  after  refraction  to  come  from 
a  point  on  the  same  side  of  and  equally  distant  from  the  axis  in 
the  other  principal  plane;  that  is,  the  determining  conditions  of 
the  principal  points  are:  (1)  that  they  must  be  conjugate;  and 
(2)  that  an  object  situated  in  one  of  these  planes  and  its  image 
situated  in  the  other  plane  must  be  equal. 

The  condition  of  equality  of  object  and  image  {the  two 
lying  on  the  same  side  of  the  axis)  after  four  refractions  is 

tan  a  —  n4  tan  a4 

as  we  have  learned  from  equation  (7).  If  we  apply  this  con- 
dition to  equation  (13),  we  derive 

■0634  f  =  —  -1127 
or 

/  =  —  i-77 

The  first  principal  point  therefore  lies  1.77  mm  behind  the  anterior 
surface  of  the  cornea. 

Second  Principal  Point. — In  equation  (12)  we  write 
—  /4  tan  a4  [f4  tan  (180  —  a)]  for  b4  and  multiply  both  terms  by  «4 : 
— k4  tan  a4  /4  =  .7415  nt  X  /  tan  a  +  5.4005  X  »4  X  tan  a. 


Appendix  339 

Since  n4  tan  a4  =  tan  a,  and  since  /  (which  is  conjugate  to 
/4)  is  —  1.77  mm,  as  has  been  found  for  the  first  principal  point, 
we  derive 

—  f<  =  —  i.3i24  n*  +  5-4005  n4 

By  reduction  and   substitution  of  its  value    (1.337)    f°r   n*  we 
derive 

/*  =  —  5.46 

The  second  principal  point  therefore  lies  5.46  mm  in  front 
of  the  posterior  surface  of  the  crystalline  lens  and  consequently 
it  lies  2.14  mm  behind  the  anterior  surface  of  the  cornea. 

First  Nodal  Point. — Since  the  nodal  rays  pass  through  a 
system  without  deviation  the  nodal  points  are  determined  by  the 
condition  of  equality  of  a  and  a4.  We  impose  this  condition  in 
equation  (13)  and  derive 

—  1.337  =  .0634  f  —  .8873 
f  =  —  7.09 

The  first  nodal  point  lies  7.09  mm  behind  the  anterior  sur- 
face of  the  cornea. 

Second  Nodal  Point. — In  equation  (12)  we  write  —  /4 
tan  at  for  &4  and  /  tan  a  for  b^ 

—  /4  tan  a4  =  .7415  f  tan  a  -\-  5.4005  tan  a 
Since  tan  a4  =  tan  a,  and  f,  the  value  found  for  the  first  nodal 
point,  is  —  7.09,  we  deduce 

f4  =  —  .14 

The  second  nodal  point  lies  .14  mm  in  front  of  the  posterior 
surface  of  the  crystalline  lens,  or  it  lies  7.46  mm  behind  the  an- 
terior surface  of  the  cornea. 

Principal  Focal  Distances. — In  accordance  with  the 
demonstration  of  Gauss,  we  can  express  the  relation  between  con- 
jugate points  after  refraction  by  a  compound  system  of  any  num- 
ber of  surfaces  by  the  same  formula  which  expresses  this  rela- 
tion after  a  simple  refraction ;  but  in  order  to  do  this  we  must 
measure  the  anterior  conjugates  from  the  first  principal  point 
and  the  posterior  conjugates  from  the  second  principal  point. 

The  anterior  principal  focal  distance  of  the  eye  is  therefore 
15.76  mm  (13.99  +  1-77)  and  the  posterior  focal  distance  is 
21.08  mm  (15.62  +  5.46). 

With  these  values  for  F  and  F'  respectively  we  may  express 
the  relation  between  conjugate  points  by  the  equation 

F     ,    F' 

or  by  any  of  the  other  forms  in  which  we  write  the  relation  be- 
tween conjugate  points  after  a  single  refraction. 


340 


Appendix 


SUMMARY 

From  summit  of  cornea  to  first  principal  point 1.77  mm 

From  summit  of  cornea  to  second  principal  point 2.14mm 

From  summit  of  cornea  to  first  nodal  point 7.09  mm 

From  summit  of  cornea  to  second  nodal  point 7.46  mm 

From  summit  of  cornea  to  anterior  focus 13.99 'mm 

From  summit  of  cornea  to  posterior  focus 23.22  mm 

Anterior  focal  distance  (measured  from  first  principal 

point) I5-76  mm 

Posterior  focal  distance  (measured  from  second  princi- 
pal point) 21.08  ww 

Cardinal  Points  of  a  Thick  Lens 

In  the  same  way  in  which  we  determine  the  cardinal  points 
of  the  eye  we  can  find  the  cardinal  points  of  a  thick  lens ;  but  as 
in  the  latter  case  there  are  only  two  refractions  we  require  only 
equations  (5a),  (5b),  and  (ua). 

Relation   between  Variation  of  Curvature   and  Astigmia 

In  the  diagram  (Fig.  146)  the  portion  above  the  optic  axis 
represents  the  meridian  of  greatest  curvature  and  the  portion 


fig.  146 


below  the  axis  represents  the  meridian  of  least  curvature  of  an 
asymmetrical  surface.  In  the  meridian  of  greatest  curvature  C 
is  conjugate  to  /,  while  in  the  meridian  of  least  curvature  0  is 
conjugate  to  /.  In  order  that  rays  from  a  point  0  may  be 
focused  at  /  their  divergence  must  be  increased  in  the  meridian 
of  greatest  curvature  so  that  in  this  meridian  they  appear  to 
proceed  from  C. 

In  the  refraction  by  the  lens  which  thus  overcomes  the 
astigmia  0  and  C  are  conjugate  points  and  the  focal  length  of 
this  lens  is  determined  by  the  equation 


OL 


C  L 


1 
~F 


(d). 


In  the  refraction  by  the  asymmetrical  surface  we  have  for 
the  meridian  of  greatest  curvature  the  equation 


+ 


n 


AC    '    A  I 


Appendix  341 

in  which  Fx  is  the  anterior  focal  distance  of  this  refraction.     In 
the  meridian  of  least  curvature  we  have  the  equation 

x  n  1 


AO   '   A  I      f.; 

in   which   F2   is   the   anterior    focal   distance   of   this   refraction. 
By  subtraction  we  derive 


AO        AC       Ft        Fx' 

If  we  disregard  the  distance  of  the  correcting  lens  from  the 
surface  equation  (d)  becomes 

1  1  1 


AO        AC        F 

and 

1  1  1 

T  ~  F~3  ~  F\- 

Therefore,  if  we  disregard  the  distance  of  the  correcting  lens 

from  the  surface  the  dioptric  power(-„-)  of  this  lens  is  equal  to 

the  difference  of  the  reciprocals  of  the  anterior  focal  distances  in 
the  two  principal  meridians. 

The  reciprocals  of  the  anterior  focal  distances  of  the  principal  meri- 
dians of  the  cornea  (~f~  An^~fr)  are  analogous  to  the  expression     \~~f~) 

which  determines  the  dioptric  power  of  a  lens,  and  it  is  customary  to 
speak  of  the  reciprocal  of  the  anterior  focal  length  of  the  cornea  as  its 
dioptric  power.  This  is  convenient  in  ophthalmometry,  but  we  should 
not  forget  that  the  diopter  is  a  unit  of  lens  measurement  only.  We  can 
not  apply  it  in  general  calculations  to  single  surface  refraction,  in  which 
the  two  focal  distances  are  unequal,  or  to  refraction  by  a  thick  lens. 

It  is  in  this  way  that  we  measure  astigmia  by  ophthal- 
mometry. The  error  which  we  incur  by  neglecting  the  distance 
of  the  correcting  lens  from  the  eye  varies  greatly  with  the  refrac- 
tion of  the  eye,  for,  as  is  apparent  from  the  diagram,  the  error  is 
greater  according  as  the  distances  A  O  and  A  C  are  less  in  pro- 
portion to  A  L. 

The  error  is  least  in  simple  astigmia,  when  one  meridian 
of  the  eye  is  emmetropic  and  the  other  hyperopic  or  myopic. 

If  under  this  condition  the  astigmia  at  the  cornea  is  /  D, 
the  convex  correcting  lens  placed  15  mm  from  the  cornea  is  .98  D, 

( : )      :  if  the  astigmia  at  the  cornea  is  3  D,  the  convex 

Viooo  +15/  fe  ° 

correcting  lens  is  2.87  D    (  —  ),  and  so  on. 

^333  +  15' 


342  Appendix 

If  a  concave  lens  is  required  to  correct  the  faulty  meridian 
i  D  at  the  cornea  corresponds  to  a  lens  correction  of   i.oi  D 

( ) ,     3  D  at  the  cornea  corresponds  to   a   lens   cor- 

\iooo  —  15/ 

rection  of  3.14  D     (  ),  and  so  on. 

\333  —  15' 

If  in  addition  to  the  3  D  of  astigmia  the  eye  has  5  D  of 
myopia  (at  the  cornea),  we  determine  the  strength  of  the  cor- 
recting lens  as  follows :  We  first  find  the  distance  A  C  which  is 
conjugate  to  A  0  (200  mm)  when  there  is  3  D  of  astigmia 
at  the  cornea 

1  1 

— w—  -003 

200  r 

f  —    125 

The  distance  A  C  is  therefore  125  mm.  We  now  ascertain 
the  strength  of  the  correcting  lens  from  the  equation 

1  1  1 

200  —  15         125  —  15         F' 

From  this  equation  we  find  the  value  of         to  be  .0036;  or 

r 

expressed  in  terms  of  the  diopter,  D  =  3.6.  The  astigmia  which 
measures  3  D  at  the  surface  of  the  cornea  therefore  requires  a 
lens  of  3.6  D  (15  mm  from  the  cornea)  when  there  coexists 
with  the  astigmia  5  D  of  myopia. 

In  the  same  way  we  can  find  the  difference  between  the  as- 
tigmia at  the  cornea  and  the  required  correcting  lens  in  other 
states  of  refraction.  The  result  of  such  calculation  for  various 
degrees  of  ametropia  is  here  given. 

Simple   Hyperopic  Astigmia 

At  the  oornea  15  mm  from  the  cornea 

iD 98  D 

3D 2.87  D 

6D 549  D 

Simple    Myopic    Astigmia 

I  D • I.OI  D 

3D 3-14  D 

6D • 6.51  D 

Astigmia  with   5   D  of  Hyperopia 

iD 84  D 

3D • 2.50  D 

6  D 47°  D 

Astigmia   with    10   D   of   Hyperopia 

iD, 64  D 

3D • 2.04  D 

6D 405  D 


Appendix  343 

Astigmia   with   5    D   of   Myopia 

At  the  cornea  15  mm  from  the  cornea 

i  D 1.17  D 

3D • 360  D 

6  D • 7.66  D 

Astigmia  with   10  D   of  Myopia 

iD 1.36  D 

3D • 4-2    D 

6D 8.8   D 

Astigmia  with   15   D  of  Myopia 

iD • 1.5    D 

3D 4.6   D 

6D • 10      D 

From  this  table  we  see  that  in  a  high  degree  of  symmetrical 
ametropia  combined  with  a  high  degree  of  astigmia  we  must 
look  for  a  marked  difference  between  the  subjective  error  and 
the  ophthalmometric  record. 

Ophthalmometry  Determination  of  Astigmia  of  the 

Crystalline  Lens 

The  rays  of  light  which  form  the  image  reflected  from  the 
anterior  surface  of  the  lens  are  refracted  as  they  enter  and  as 
they  emerge  from  the  cornea ;  and  the  rays  which  form  the  image 
reflected  from  the  posterior  surface  are  refracted  not  only  at  the 


£x- 


l-y^k.'-' 


cornea,  but  also  at  the  anterior  surface  of  the  lens.  The  radii  of 
the  surfaces  of  the  lens  as  they  are  modified  by  refraction  are 
called  the  apparent  radii. 

The  effect  of  these  refractions  on  the  anterior  lens  sur- 
face regarded  as  a  mirror  is  shown  in  Fig.  147.  The  surface  is 
displaced  forward  from  A  to  A1  and  the  center  is  displaced  back- 
wards from  C  to  Cj.  In  the  corneal  refraction  A  and  Ax  are  con- 
jugate points,  as  are  also  C  and  C\. 

By  applying  the  equation  for  conjugate  points 

on  the  basis  of  a  radius  of  7.8  mm  for  the  cornea,  a  distance  of 
3.5  mm  from  the  anterior  surface  of  the  cornea  to  the  lens,  and  a 


344  Appendix 

refractive  index  of  1.337  f°r  the  aqueous,  I  have  derived  the 
following  relation  between  the  apparent  and  actual  radii. 

Radius  Apparent  Radius  Magnification 

8.5    mm 1 1.6  mm 1.36 

9        "    12.6   "    1.40 

95     "    137   "    1-44 

10        "    14.8   "    1.48 

10.5  "  16  "  1.52 

"  "  173  "  1.57 

11.5  "  18.6  "  1.61 

12  "  20.1  "  1.67 

12.5  "  21.6  "  173 

In  order  to  ascertain  the  amount  of  error  which  might  be 
incurred  by  basing  the  recording  scale  of  the  ophthalmometer 
upon  the  foregoing  relations,  I  have  determined  the  variation  of 
refractive  effect  which  occurs  with  the  ordinary  variations  in  the 
curvature  of  the  cornea  and  in  the  distance  between  the  cornea 
and  the  lens. 

(1).  //  the  distance  between  the  surfaces  is  3.5  mm,  zvhile 
the  radius  of  the  cornea  is  8.4  mm,  I  derive  the  follouring  re- 
lations: 

Apparent  Radius  Radius 

12.6  mm 9.3  mm 

16       "    10.9    " 

20.1     "    12.5    " 

As  in  ophthalmometry  of  the  cornea  the  reciprocal  of  the 

anterior  focal  length    (-^)    is  taken  as  the  dioptric  equivalent 

of  the  corneal  refraction,  so,  as  I  shall  subsequently  show,  the 
same  expression  represents  approximately  the  dioptric  equivalent 
(for  the  purpose  of  measuring  astigmia)  of  the  anterior  surface 
of  the  lens.  By  thus  expressing  the  dioptric  value  we  make  the 
following  comparison : 

Cornea  7.8  mm  Cornea  8.4  mm 

Apparent  Radius  Radius  Radius 

12.6  mm  9  mm  (8.3  D)  9.3  mm  (8  D) 
20.1  mm                  12  mm  (6.2  D)                   12.5  mm  (6  D) 


Difference  in  diopters 2.1  D  2D 

From  this  we  see  that  if  a  difference  of  three  millimeters 
of  radius,  as  determined  in  the  two  principal  meridians,  should 
occur,  the  error  which  would  result  from  using  a  scale  con- 
structed on  average  measurements  would  be  only  one-tenth  of  a 
diopter. 

If  the  radius  of  the  cornea  were  7.8  mm  in  one  meridian  and 
8.4  mm  in  the  other — that  is,  if  there  were  3  D  of  corneal  as- 


Appendix  345 

tigmia,  and  if  the  anterior  surface  of  the  lens  were  symmetrical, 
about  .25  D  of  apparent  astigmia  in  the  opposite  sense  as  the 
corneal  astigmia  would  be  produced.  If  the  radius  of  the  lens 
surface  varied  in  the  different  meridians  between  the  limits  above 
shown,  the  astigmia  would  be  overestimated  or  underestimated 
by  about  .25  D. 

(2)  /  next  apply  the  same  method  to  ascertain  the  possible 
error  when  the  radius  of  tflie  cornea  is  7.3  mm  (46  D),  while  the 
distance  from  the  cornea  to  the  lens  remains  3.5  mm. 

Cornea  7.3  mm  Cornea  7.8  mm 

Apparent  Radius  Radius  Radius 

12.6  mm 8.6  mm  (8.7  D) 9  mm  (8.3  D) 

20.1  mm 11.5  mm  (6.5  D) 12  mm  (6.2  D) 

Difference  in  diopters 2.2  D 2.1  D 

As  before,  the  error  from  using  a  scale  constructed  with 
average  measurements  is  negligible  as  long  as  the  cornea  is  sym- 
metrical;  if  the  radius  of  the  cornea  were  7.8  mm  (43D  )  in 
one  meridian  and  7.3  mm  (46  D)  in  the  other,  the  resulting  3  D 
of  corneal  astigmia  would  entail  an  error  of  from  .25  D  to  .4  D 
in  the  measurement  of  the  lens.  This  error  is  slightly  more  than 
that  which  would  result  on  the  basis  of  the  larger  radius 
(8.4  mm),  but  we  should  get  sufficient  accuracy  by  assuming  that 
3  D  of  corneal  astigmia  would  produce  an  apparent  opposite 
astigmia  of  .37  D,  or  that  each  diopter  of  corneal  astigmia  would 
produce  an  apparent  opposite  astigmia  of  .12  D. 

(3)  With  an  average  radius  of  the  cornea  (7.8  mm)  what 
would  be  the  error  from  variation  in  the  distance  between  the 
cornea  and  the  lens:?    Proceeding  as  before,  I  find  these  relations : 

Distance  from  Cornea  to  Lens 
[3  mm  3.5  mm  4  mm  J 

Apparent  Radius  Radius  Radius  Kadius 

12.6  mm. ...  9.2  mm  (8.1  D)  . . . .  9  mm  (8.3  D)  . . . .  8.7  mm  (8.6  D) 

20.1  mm 12.3  mm  (6.1  D) 12  mm  (6.2  D) 11.6  mm  (6.4  D) 

Difference  in  diopters  2    D 2.1  D 2.2  D 

The  error  arising  from  variation  in  the  depth  of  the  anterior 
chamber  would  not,  therefore,  exceed  one-tenth  of  a  diopter  in 
a  variation  of  three  millimeters  of  radius. 

(4)  The  greatest  error  in  the  measurement  of  the  actual 
radius  would  occur  if  we  had  a  large  radius  of  the  cornea  com- 
bined with  a  shallow  anterior  chamber  or  a  small  radius  of  the 
cornea  with  a  deep  anterior  chamber.  In  order  to  determine  the 
possible  error  in  the  measurement  of  astigmia  I  have  applied 
the  formula  for  conjugate  points  (a)  with  a  corneal  radius  of 
8.4  mm  and  a  distance  of  3  mm  between  the  two  surfaces  and 


346  Appendix 

(b)  with  a  corneal  radius  of  7.3  mm  and  a  distance  of  4  mm  be- 
tzueen  the  surfaces.    In  this  way  I  derive  the  following  relations : 

Radius  ol  cornea,  8.  4  mm  ;  Had  i  us  of  cornea,   7.8mm;    dis-  Radius  of  cornea,  7.3  mm  ; 
distance  betweeu  sur-                  tance  between  surfaces,  distance  between  sur- 

faces, 3  mm  3.5  mm  face?,  4  mm. 

Apparent  Radius  Radius  Radius  Radius 

12.6  mm 9.5  mm  (7.8  D) gmm  (8.3  D) 8.3  mm  (9    D) 

20.1  mm 12.8  mm  (5.8  D) 12  mm  (6.2  D) 11     mm  (6.8  D) 

Difference  in  diopters  2.    D 2. 1  D 2.2  D 

A  review  of  the  foregoing  relations  shows  that  although  we 
could  not  rely  upon  average  measurements  for  determining  the 
exact  radius  of  curvature  of  the  anterior  surface,  such  average 
measurements  would  be  sufficient  for  the  construction  of  a  scale 
for  measuring  the  astigmia  resulting  from  asymmetry  of  this 
surface.  Furthermore,  when  we  recall  the  fact  that  the  radius 
of  the  cornea  very  rarely  differs  by  more  than  one  millimeter  in 
the  two  principal  meridians  and  that  this  amount  of  difference 
in  the  anterior  surface  of  the  lens  produces  only  two-thirds  of  a 
diopter  of  astigmia,  it  is  apparent  that  such  a  degree  of  asym- 
metry of  this  surface  as  ordinarily  occurs  gives  rise  to  a  very 
small  amount  of  astigmia. 

In  view  of  the  unimportance  of  the  anterior  surface  of  the 
lens  as  a  factor  in  the  etiology  of  astigmia  it  is  useless  to  enter 
into  the  investigation  of  the  slight  distorting  effect  which  corneal 
astigmia  would  have  upon  the  principal  meridians  of  the  anterior 
lens  surface  when  the  meridians  of  the  corneal  and  lenticular 
astigmia  are  obliquely  inclined. 

The  apparent  radius  of  the  posterior  surface  of  the  lens  does 
not  appreciably  differ  from  the  actual  radius.  By  applying 
the  formula  for  conjugate  foci  to  the  two  refractions,  using  the 


fig    148 

data  of  the  schematic  eye,  I  have  found  that  the  surface  and  its 
center  are  each  displaced  forward  about  two-tenths  of  a  milli- 
meter, so  that  the  curvature  of  the  apparent  surface  is  the  same 
as  that  of  the  actual  surface  (Fig.  148). 

Relation  between  Astigmia  produced  at  the  Anterior 
Surface  of  the  Crystalline  Lens  and  the  Correcting  Lens 
Placed  in  front  of  the  Cornea. — The  astigmia  which  results 


Appendix  347 

from  asymmetry  of  the  anterior  lens  surface  is  expressed  by  the 
difference  between  the  reciprocals  of  the  anterior  focal  lengths 

in  the  principal  meridians  (■-=. -=-)  »  as  in  corneal  astigmia, 

but  the  application  of  the  formula  for  conjugate  points  shows  that 
the  correcting  lens,  if  placed  in  contact  with  the  cornea,  would  be 
n  (1.337)  times  the  dioptric  value  of  the  astigmia  at  the  asym- 
metric surface,  provided  we  neglect  the  distance  between  the 
crystalline  lens  and  the  cornea.  But  this  distance  cannot  be  dis- 
regarded without  appreciable  error.  I  have  determined  from  the 
equation  for  conjugate  points  the  correcting  lens  which  would  be 
required,  using  the  measurements  of  the  schematic  eye,  for 
various  degrees  of  asymmetry  of  the  anterior  lens  surface  in 
simple  astigmia,  in  hyperopia  of  5  D,  and  in  myopia  of  10  D, 
and  I  have  found  that  the  correcting  lens  placed  in  contact  with 
the  cornea  is  very  nearly  expressed  in  diopters  by  the  formula 

1  1  .  , 

-= =r,  as  in  corneal  astigmia. 

Relation  between  Astigmia  produced  at  the  Posterior 
Surface  of  the  Crystalline  Lens  and  the  Correcting  Lens 
Placed  in  front  of  the  Cornea. — In  deducing  this  relation  we 
first  have  to  find  the  equivalent  lens  if  it  were  placed  in  front 
of  the  anterior  surface  of  the  crystalline  lens  and  from  this  de- 
termine the  lens  which  would  be  required  in  front  of  the  cornea, 
as  in  the  previous  case.  If  we  could  neglect  the  distance  from 
the  posterior  lens  surface  to  the  cornea,  the  correcting  lens  would 
be  expressed  by  the  difference  of  dioptric  power  in  the  two  prin- 
cipal meridians  multiplied  by  the  refractive  index  of  the  crystal- 

line  lens    (  ,-.-  —  ~\     ;  but,  owing  to  the  distance  at  which  the 

lens  must  be  removed  from  the  surface  under  measurement,  a 
weaker  lens  is  required  than  is  indicated  by  this  expression.  In 
the  same  way  as  for  the  anterior  lens  surface  I  have  applied  the 
formula  for  conjugate  points  to  asymmetry  of  the  posterior  sur- 
face in  simple  astigmia,  in  hyperopia  of  5  D  and  in  myopia  of 
10  D,  and  I  have  found  that  nine-tenths  of  the  astigmia  as 
measured  by  the  expression 


^  ^ 


approximately  represents  the  power  of  the  correcting  lens  in  all 
of  these  conditions.  The  scale  of  my  ophthalmometer  has  been 
constructed  in  accordance  with  these  findings. 


INDEX 


A 

Page 

Abduction   146 

Aberration 40 

In  skiascopy 188 

Absorption   of   light    22 

Abversion    146 

Accommodation 62,   128 

Compensatory,    in    astigmia....   240 

Helmholtz's  theory  of 132 

Loss    of,    in    aphakia 266 

Measurement  of    74 

Near-point  of 139 

Paralysis  of    264 

Range  of 139 

Relative 155 

Reserve    140 

Spasm   of 262 

In  etiology  of  myopia 218 

Time  required  for  variation  of.    138 

Tscherning's  theory  of 135 

Variation   of,   with  age 139 

Adduction   146 

Advancement  of  muscle 302 

Adversion   146 

After   images 151 

Amblyopia  ex  anopsia  (from  disuse). 

281,  294 

Amblyoscope   257 

Ametropia 61 

Length   of  axis  in 80 

Measurement  of 76 

Use  of  lenses  in 73 

Angle  alpha   124 

Critical    34 

Gamma     124 

Anisometropia    253 

Anophoria   and   anotropia 268,   304 

Aphakia,  refractive  condition  in....      81 
Enlargement    of    images    in....      79 

Aphakic  eye   61 

Aqueous  humor   117,   119 

Asthenopia    203 

In    anisometropia 255 

In  astigmia 246 

In   hyperopia    203 

In  myopia 227 

_  In  presbyopia 259 

Astigmia   62,  237 

Classifications  of 241 

Corneal    238 

Correction  of 83 

Determination    of,    by    ophthal- 
mometry   1 08,   340 

By  ophthalmoscopy 183 

By  skiascopy 186 

By  test-lenses  and  charts 176 

Diagnosis   of    247 

Distortion  of  images  in 83 

Dynamic  compensatory    240 

Irregular    83,  237 

Lenticular 239 

Produced    by    oblique    spherical 

refraction    69 

By  prismatic  refraction 71 

Regular    »3,  237 

Symptoms  of    244 

Treatment    of 248 

Vision  in 244 


Page 

Asymmetrical  refraction   64 

Atropin,    use   of,    as   cycloplegic. .  .  .  171 

In  amblyopia 297 

Atropinism 172 

Axial   length,    in   ametropia 80 

Of  the  normal  eye 128 

Axis    of    cylindrical    lens 67 

Determination   of    85 

Methods    of    indicating 178 

Of  optical  system   43 


B 


Bandaging  for  developing  amblyopic 

eye 297 

Bar-reading 297 

Bifocal   lenses    262 

Binocular  vision 149 

Brachymetropia 214 

Tests   of    287 


Capsule  of  Tenon   143 

Cardinal      points      and     planes, 

compound  system    55 

Of  lenses 49,  340 

Of  single  surfaces 43 

Of  the  eye 334 

Cataract,    as    a    form    of    senile    de- 
generation     123 

Center,   optic    43 

Of  rotation  lens    47 

Centrad 29 

Check  ligaments  . . 143 

Choroidal  and  retinal  pigment 127 

Chromatic    aberration    41 

In  optometry   163 

Ciliary  muscle    131 

Region,  anatomy  of   131 

Circle   of  least  confusion 66 

Clinoscope 280 

Clock-dial  chart 17b 

Cocain,  use  of,  with  homatropin.  .  .  .  173 

Color  glass  test 274 

Color  sensation    16 

Colors   of  the    spectrum    17 

Dispersion  of z8 

Compound  hyperopic  astigmia jS 

Compound    optical    system    54 

Conical    cornea*     as    cause    of    my- 
opia   (Keratoconus) 214 

Operative  treatment  of 235 

Conjugate  foci  and  focal  distances..  37 
Algebraic  relation  between,  com- 
pound systems,  lenses  ....49,  33J 

Deviation,   paralytic   322 

Movements 1 50 

Reflection    . . 53 

Single  refracting  surfaces. .  .41,  328 

Spastic 305 

Conus 220 


349 


35° 


Index 


Page 

Convergence 153 

Relative 155 

Deficiency     of — See     Deficiency 

of   convergence. 
Excess   of — See   Excess   of   con- 
vergence. 

Far-point  of 154 

Measurement  of 153.  279 

Near-point  of 154 

Paralysis  of 323 

Convergence   accommodation    155 

Con  j  uncti  va 1 1 1 

Cornea    55,    ill,   112,  118 

Corneal  curvature,  determination  of, 

by  keratometry    100 

Corpuscular  theory  of  light 14 

Corresponding    points    158 

Cover  test  for  heterophoria 273 

Critical  angle   34 

Crystalline  lens 55 

Curvature    of,    in    accommoda- 
tion  129,  130,  135 

Dioptric   power   of    122 

Enlargement     of     images     pro- 
duced by  removal  of 79 

Equivalent     refractive     index 

of 56,  121 

Loss  of  transparency  of,  in  old 

age    123 

Oblique    position    of,    as    cause 

of  astigmia    194,  239 

Refractive  effect  of  removal  of.  81 

Spectrum  of _. .  122 

Cyclophoria    and    cyclotropia 

269,  288,  304 
Cycloplegia — See     Paralysis     of     ac- 
commodation. 

Artificial    171 

Cycloplegics 171 

Use  of,  in  astigmia   247 

In   hyperopia    206 

In    myopia    229 

In   spasm   of  accommodation..  264 

In  strabismus 297 

Cylindrical  lens 67 

Determination  of  axis  of 85 

Distortion    of    images    produced 

by 84 

Methods  of  indicating  axis  of..  178 

Cylindrical  lenses,  combination  of.  .  68 


Decentering  of  lenses    295 

Declination   269 

Deficiency   of  convergence 299 

Diagnosis  of 300 

Symptoms  of    300 

Treatment  of 301 

Deviation,  by  prism 26,  326 

Primary 2ji 

Secondary 271 

Diffraction    19 

Diopter    50 

Diplopia,  artificial 272 

Analysis  of 317 

Binocular 269 

In  non-paralytic  strabismus   .  .  .  294 

In    paralytic    strabismus    310 

Monocular 263 

Disorders      of      motility,      non-para- 
lytic   267 

Caused    by    mechanical    impedi- 
ment    206 

Paralytic 308 

Dispersion  of  colors 28 


Page 

Divergence    164 

Measurement  of 279 

Divergent   strabismus    (squint) — See 
Strabismus. 

Dynamic  astigmia   240 

Refraction     127 

E 

Emmetropia    127 

Errors  of  refraction 161 

Esophoria   and   esotropia    (excess  of 

convergence)    268 

Ether  (of  space) 14 

Euthophoria 268 

Excess  of  convergence    291 

Diagnosis  of 294 

Etiology  of 292 

Operative    298 

Symptoms  of   293 

Treatment  of 294 

Exophoria  and  Exotropia  (deficiency 

of   convergence) 268 

External  coat  of  eye 112 

Rectus 144,  146 

Paralysis  of    312 

Extrinsic  muscles   144 

Eye   55,  in 

Aphakic 61 

Model  for  skiascopy 190 

Normal in 

Reduced    59 

Refraction  of 129 

Schematic   59 


F 

False  image .•  270 

Far-point  of  accommodation 75 

Of  convergence   154 

Farsightedness 196 

Fixation,    binocular    149 

Field    of    149 

Measurement  of 286 

Focal   interval    (Sturm's) 66 

Lines 66 

Foci — See   Conjugate  foci. 

Fovea 116 

Fraunhofer  lines 18 

Fusion,  breadth  of   271 

Fusion  center,  defective  development 

of    293 


G 

Galileo's  telescope  in   optometry....    162 

Gamma 124 

Graefe's   diplopia   test    275 

Method    of    measuring    strabis- 
mus       281 

Touch  test    311 


H 

Headache,  as  symptom  of  eyestrain.  204 
Helmholtz's    theory    of    accommoda- 
tion   132 

Heterophoria    267 

Heterotopia    (strabismus) '.  267 

Homatropin    1 72 

Horopter ; 158 

Hypermetropia 196 


Index 


35i 


Page 

Hyperopia     61,  79,  196 

Absolute    202 

Axial    196 

Axial  length  in    198 

Correction   by   convex    lens....  73 

Curvature    196,  197 

Degree  of 199 

Diagnosis    of    205 

Facultative    202 

Index     196 

Latent    201 

Manifest 201 

Strabismus  in 204 

Symptoms  of    202 

Total    201 

Treatment  of 207 

Vision  in 202 

Hyperphoria 268 

Hypertropia    Cvertical   strabismus) .  .  302 


I 

Image,    relative    size    of    ....43.   44,  58 

Formation   of    20,   42,   47,  5  7 

In  astigmia 66 

Mental     rectification     and     pro- 
jection of    57 

Size   of,  as  affected  by  correct- 
ing lens  in   ametropia    76 

By  removal  of  crystalline  lens  79 

Inch   system   of  numbering  lenses..  49 
Indirect   ophthalmoscopy — See   Oph- 
thalmoscopy. 

Inferior  oblique  muscle 145,  148 

Paralysis  of    315 

Rectus    1 44,  146 

Paralysis  of 314 

Insensitiveness      of      periphery      of 

retina 124 

Internal  rectus 144.  146 

Paralysis  of    312 

Intrinsic    muscles    144 

Iris 126 

J 

Jaeger's  test-type 260 


K 

Katophoria   and   katotropia 268,  304 

Keratoconus 214 

Keratometry 106 

Kinescopy   165 

L 

Landolt's   optotype    168 

Law  of 150 

Reflection    32 

Refraction    (Snell's   law) 23 

Lenses,  asymmetrical   73 

Bifocal : 262 

Cardinal    points    of    49 

Concave 48 

Convex    45 

Crystalline — See  Crystalline  lens. 

Cylindrical    67 

Determination     of     power     and 

center  of 169 

Optic  center 43 

Periscopic    45 

Spectrum 122 


Page 

Spherical    44,  73 

Toric    67 

Lens-measure   1 70 

Lenses,  collective   45 

Dispersive 48 

Effect  of,   on  size  of  image ....  76 

Neutralization   of    169 

Numeration  of 49 

Prescription   of    ......212,  233,  249 

Verification    of    .  .  .' 213 

Lenticonus    215 

Light    13 

Luminosity    18 

M 

Macropsia   263 

Macula   116 

Maddox  prism 275 

Rod  test    277 

Tangent  scale 284 

Magnifying  glass 78 

Medium     22 

Meniscus     45 

Meter-angle 30,  154 

Minimum  deviation   27,  327 

Motions  of  the  Eye   146 

Muscae  volitantes 124 

Muscles  of  the  Eye  144 

Muscular  equilibrium 159 

Imbalance   291 

Mydriatics 171 

Myopia    62,  79,  254 

Axial    215 

Two   types   of    223 

Treatment  of 230 

Operative    treatment    of 233 

Axial  length  in   216 

Correction  of,  by  concave  lens.  75 

Curvature   214 

Operative  treatment  of 235 

Diagnosis    of    229 

Index 215 

Prophylaxis  of 230 

Statistics   of 226 

Symptoms  of   227 


N 

Near-point    of    accommodation    ....  139 

Of  convergence 154 

Nearsightedness 214 

Neutralization   of  lenses 169 

Nodal  Point 43 

Of  lens    47 

Points    of    compound    system..  55 

Of   the   eye    .  :59.  339 

Non-paralytic  disorders  of  motility.  291 

Normal    eye,    motility    of    143 

Refraction  of 1  1  1 

Numeration    of   lenses    49 

Of  prisms » 28 

Nystagmus    305 

o 

Oblique   muscle,   inferior    145,  14S 

Paralysis  of    3 '  5 

Superior 1 45,  148 

Paralysis  of   3 '  5 

Refraction 69 

Occlusion     of     the     better     eye     in 

strabismus 247 

Of  paralyzed  eye 321 

Oliver's  test-types 260 


352 


Index 


Page 

Opera-glass  optometer   162 

Ophthalmodynamometer   .280 

Ophthalmo-phakometer 107 

Ophthalmometer 100,    190 

Ophthalmometry 99,    190 

Ophthalmoplegia    308 

Ophthalmoplegic   migraine    309 

Ophthalmoscopy 87 

Direct   90,    1 79 

Indirect    89,    183 

Ophthalmotrope 152 

Optic  center 43 

Of  lens   47 

Optics    13 

Optometry,  motor 267 

Refractive   161 

Orientation     (mental     projection    of 
retinal  image)    57 

Of  false  image 271 

Orthophoria    267 


Parallax    test    274 

Paralysis,   combined    316 

Of  accommodation 264 

Of  convergence   323 

Of  divergence    324 

Of  external  rectus   312 

Of  inferior   oblique    315 

Of  inferior  rectus 314 

Of   internal   rectus    312 

Of  ocular  muscle    308 

Determination  of  lesion  of  ....    319 

Diagnosis  of 316 

General    symptoms   of    309 

Treatment  of 320 

Of  superior  oblique    315 

Of  superior  rectus    312 

Of  third   nerve    315 

Paralytic  disorders  of  motility    ....    308 

Strabismus    310 

Pencil   of   light    19 

Periscopic  lenses 45,   212,   233 

Phakometry   106,   3^3 

Phorometer    276,  285 

Placido's  disk 191 

Point    of    reversal     Q2 

Polyopia    263 

Posterior  staphyloma   219 

Anatomical  and  ophthalmoscopic 

characteristics  of 222 

Theories  as  to  origin  of 221 

Presbyopia   62,  259 

Prescription  of  lenses    ....212,  233,  249 

of  prisms 295 

Primary  axis    43 

Deviation     271 

Position  of  the  eyes   146 

In  ophthalmometry 192 

Principal    foci    and    focal    distances 

of  the  eye 50 

Of  lenses 46.     48 

Of    single    surfaces    37 

Focus,   in   reflection    53 

Meridians    64 

Point    43 

Points  of  the  eye 59 

Prism,  Maddox 275 

Rotary 276 

Wollaston    102 

Prism,   convergence    280 

Prism,  diopter   29 

Prism,  exercises 297,   301 

Prismatic  action  of  lenses 211 

Refraction,  asymmetry  of 71 

Prisms,   25,   326 


Page 

<.  ombination  of    30 

Numeration  of 28 

Prescription   of    295 

Use  of,  in  esophoria 295 

In   exophoria    301 

Hyperphoria 303 

In  paralysis    321 

Pupil    126 

Purkinje's  images 100 

R 

Rays 19 

Recti  muscles 144 

Rectification       and       projection      ol 

retinal  images 57 

Reduced   eye    59 

Reflection     31,  51 

Algebraic  formula  of 53 

Law   of    32 

Total    33 

Refracting  angle  of  prism 26 

Refraction 22 

Asymmetrical      64 

Collective    (convergent)     39 

Dispersive    (divergent)     40 

Dynamic    127 

Of  the  eye 127 

Methods  of  determining 161 

Formation  of  images  by 42 

Through     plate     with     parallel 

surfaces 25 

By  prism 25 

At  spherical  surfaces 36 

Static 127 

Toric    64 

Refractive  index   23 

Retina    115 

Rotation  of  the  eye    146 

s 

Scheiner's  experiment   162 

Schematic    eye    59,  334 

Sclera  in,  113 

Scissors    movement     180 

Secondary   axis    43 

Deviation 271 

Effect  of  concave  lenses 233 

Of  convex  lenses    210 

Position  in  ophthalmometry....  192 

Shadow  test   93 

Shortsightedness    214 

Skiascopy,     optical     principles     of..  92 

Practical  application  of 183 

Spasm  of  accommodation    262 

Spasmodic  conjugate  deviation 305 

Spectrum 17 

Of  lens 122 

Staphyloma — See    Posterior    stapny- 
loma. 

Static  refraction    127 

Stenopaeic  disk 175 

Lens  test  for  heterophoria   ....  279 
Stereoscopic  exercises  in  convergent 

strabismus 296 

In   divergent   strabismus    301 

In  paralysis   321 

Strabismus      268 

Convergent 291 

Treatment    of — See     Excess    of 
convergence. 

Divergent    290 

Treatment    of — See     Deficiency 
of   convergence. 

In   hyperopia    204 

Measurement  of 281 


Index 


353 


Page 

In    myopia 228 

Paralytic   3io 

Vertical 302 

Sub-duction    U6 

Superior   oblique   muscle    145.    J48 

Paralysis  of   3 1 5 

Rectus  muscle i44»   146 

Paralysis  of   312 

Supra-duction    J4° 

Supra-version   . .  .  ._ :4° 

Surfaces  and  media  117 

Sursumduction     302 

T 

Telescope    I0° 

Tenon's  capsule J43 

Tenotomy    3°2 

Test-types,  Jaeger 2°° 

Landolt J°8 

Oliver    2°°. 

Snellen    !°6 

Thomson's   ametrometer    i°5 

Tilting   of   lenses    7° 

Tinted  glasses    233 

Toric  lenses °7 

Surface    64 

Torsion    146,   15° 

Trial   lenses    •  •  •      %7 

Tropometer   28S.  2»o 


u 


Uvea 


Page 

.    114 


V 

Velocity     of     light     and     vibratory 

period    18 

Verification  of  lenses 213 

Of    prisms    296 

Vertical  imbalance    302 

Visual  acuteness   165 

Visual  angle 58 

Vision    13 

Binocular    149 

Vitreous    123 

w 

Wave-front 18 

Wave-length 18 

Wave-theory 14 

Waves 14 

Superposition  of 20 

Wollaston  Prism 102 

Y 

Young-Helmholtz  theory  of  colors..  16 

Young's  optometer 163 


Physiologic  Optics 

Ocular  Dioptrics  —  Functions  of  the 

Retina  —  Ocular  Movements  and 

Binocular  Vision 

By  DR.   M.   TSCHERNING 

Director  of    the    Laboratory  of    Ophthalmology 
at  the  Sorbonne,  Paris 

<** 

AUTHORIZED   TRANSLATION 

By  CARL  WEILAND,  M.D. 

Former  Chief  of  Clinic  in  the  Eye  Department  of  the 
Jefferson  College  Hospital,  Philadelphia,  Pa. 

THIS  book  is  recognized  in  the  scientific  and  medical 
world  as  the  one  complete  and  authoritative  treatise 
on  physiologic  optics.  Its  distinguished  author  is 
admittedly  the  greatest  authority  on  this  subject, 
and  his  book  embodies  not  only  his  own  researches,  but  those 
of  the  several  hundred  investigators  who,  in  the  past  hundred 
years,  made  the  eye  their  specialty  and  life  study. 

Tscherning  has  sifted  the  gold  of  all  optical  research 
from  the  dross,  and  his  book,  as  now  published  in  English, 
with  many  additions,  is  the  most  valuable  mine  of  reliable 
optical  knowledge  within  reach  of  ophthalmologists.  It  con- 
tains 380  pages  and  212  illustrations,  and  its  reference  list 
comprises  the  entire  galaxy  of  scientists  who  have  made 
the  century  famous  in  the  world  of  optics. 

The  chapters  on  Ophthalmometry,  Ophthalmoscopy, 
Accommodation,  Astigmatism,  Aberration  and  Entoptic 
Phenomena,  etc. — in  fact,  the  entire  book  contains  so  much 
that  is  new,  practical  and  necessary,  that  no  refractionist  can 
afford  to  be  without  it. 

Bound  in  Cloth.  380  Pages,  212  Illustrations. 

Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price 

$2.50  (10s.  5d.) 

Published  by 
THE  KEYSTONE   PUBLISHING  COMPANY 

809-811-813  NORTH  19th  STREET, 
PHILADELPHIA,  U.  S.  A. 


Tests  and  Studies 

of  the  Ocular 

Muscles 


By  ERNEST  E.  MADDOX,  M.D.,  F.R.C.S.,  Ed. 

Ophthalmic  Surgeon  to  the  Royal  Victoria  Hospital,  Bournemouth,  England  ; 
formerly  Syme  Surgical  Fellow,  Edinburgh  University 

THIS  book  is  universally  recognized  as  the 
standard  treatise  on  the  muscles  of  the  eye, 
their  functions,  anomalies,  insufficiencies,  tests 
and  optical  treatment. 
All  opticians  recognize  that  the  subdivison  of  refractive 
work  that  is  most  troublesome  is  muscular  anomalies. 
Even  those  who  have  mastered  all  the  other  intricacies 
of  visual  correction  will  often  find  their  skill  frustrated 
and  their  efforts  nullified  if  they  have  not  thoroughly 
mastered  the  ocular  muscles. 

The  eye  specialist  can  thoroughly  equip  himself 
in  this  fundamental  essential  by  studying  the  work  of 
Dr.  Maddox  who  is  known  in  the  world  of  medicine 
as  the  greatest  investigator  and  authority  on  the  sub- 
ject of  eye  muscles. 

The  present  volume  is  the  second  edition  of  the 
work,  specially  revised  and  enlarged  by  the  author.  It 
is  copiously  illustrated  and  the  comprehensive  index 
greatly  facilitates  reference. 

Bound   in   Silk   Cloth  —  261  Pages  —  110  Illustrations. 
Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price 

$1.50  (6s.  3d) 

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The 

Principles  of  Refraction 

in  the  Human  Eye,  Based  on  the 
Laws  of  Conjugate  Foci 

By  SWAN  M.  BURNETT,  M.D.,  PH.D. 

Formerly  Professor  of  Ophthalmology  and  Otology  in  the  Georgetown 
University  Medical  School ;   Director  of  the  Eye  and  Ear  Clinic, 
Central  Dispensary  and  Emergency  Hospital ;   Ophthalmo- 
logist to  the  Children's  Hospital  and  to  Providence 
Hospital,  etc.,  Washington,  D.  C. 

IN  this  treatise  the  student  is  given  a  condensed  but 
thorough  grounding  in  the  principles  of  refraction 
according  to  a  method  which  is  both  easy  and  funda- 
mental. The  few  laws  governing  the  conjugate  foci 
lie  at  the  basis  of  whatever  pertains  to  the  relations  of 
the  object  and  its  image. 

To  bring  all  the  phenomena  manifest  in  the  refraction  of 
the  human  eye  consecutively  under  a  common  explanation  by 
these  simple  laws  is,  we  believe,  here  undertaken  for  the  first 
time.  The  comprehension  of  much  which  has  hitherto  seemed 
difficult  to  the  average  student  has  thus  been  rendered  much 
easier.  This  is  especially  true  of  the  theory  of  Skiascopy, 
which  is  here  elucidated  in  a  manner  much  more  simple  and 
direct  than  by  any  method  hitherto  offered. 

The  authorship  is  sufficient  assurance  of  the  thorough- 
ness of  the  work.  Dr.  Burnett  was  recognized  as  one  of  the 
greatest  authorities  on  eye  refraction,  and  this  treatise  may 
be  described  as  the  crystallization  of  his  life-work  in  this  field. 
The  text  is  elucidated  by  24  original  diagrams,  which 
were  executed  by  Chas.  F.  Prentice,  M.E.,  whose  pre-emi- 
nence in  mathematical  optics  is  recognized  by  all  ophthalmol- 


ogists. 


BOUND    IN    SILK    CLOTH 
Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price 

$1.00  (4s.  2d.) 

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Ophthalmic  Lenses 

Dioptric  Formulae  for  Combined  Cylindrical 

Lenses,  The  Prism-Dioptry  and 

Other  Original  Papers 

By  CHARLES  F.  PRENTICE,  M.E. 

A  new  and  revised  edition  of  all  the  original  papers  of  this  noted  author, 
combined  in  one  volume.  In  this  revised  form,  .with  the  addition  of  recent 
research,  these  standard  papers  are  of  increased  value.  Combined  in  one 
volume,  they  are  the  greatest  compilation  on  the  subject  of  lenses  extant. 
This  book  of  over  200  pages  contains  the  following  papers: 

Ophthalmic  Lenses. 

Dioptric  Formulae  for  Combined  Cylindrical  Lenses. 

The  Prism-Dioptry. 

A  Metric  System  of  Numbering  and  Measuring  Prisms. 

The  Relation  of  the  Prism-Dioptry  to  the  Meter  Angle. 

The  Relation  of  the  Prism-Dioptry  to  the  Leus-Dioptry. 
The  Perfected  Prismometer. 
The  Prismometric  Scale. 
On  the  Practical  Execution  of  Ophthalmic  Prescriptions 

involving  Prisms. 
A  Problem  in  Cemented  Bi-Focal  Lenses,  Solved  by  the 

Prism-Dioptry. 
Why  Strong  Contra-Generic  Lenses  of  Equal  Power  Fail 

to  Neutralize  Each  Other. 
The  Advantages  of  the  Sphero-Toric  Lens. 
The  Iris,  as  Diaphragm  and  Photostat. 
The  Typoscope. 
The  Correction  of  Depleted  Dynamic  Refraction  (Presbyopia). 

PRESS  NOTICES  OF  THE  ORIGINAL  EDITION : 

OPHTHALMIC  LENSES 

"  The  work  stands  alone,  in  its  present  form,  a  compendium  of  the  various  laws  of 
physics  relative  to  this  subject  that  are  so  difficult  of  access  in  scattered  treatises." 

— Keir  England  Medical  Gazelle. 

"  It  is  the  most  complete  and  best  illustrated  book  on  this  special  subject  ever  published." 

— Horological  Review,  New  York. 

"Of  all  the  simple  treatises  on  the  properties  of  lenses  that  we  have  seen,  this  is  incom- 
parably the  best.  .  .  .  The  teacher  of  the  average  medical  student  will  hail  this 
little  work  as  a  great  boon."        — Archives  of  Ophthalmology,  edited  by  H.  Knapp,  M.D. 

Round  in  Silk  Cloth.  110  Original  Diagrams. 

Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price 

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809-811-813  NORTH  19th  STREET 
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Clinics  in  Optometry 

By  C.  H.  BROWN,  M.  D. 

Graduate  University  of  Pennsylvania  ;  Professor  of  Principles  and 

Practice  of  Optometry  ;  formerly  Physician  to  the 

Philadelphia  Hospital ;   Author  of  the 

Optician's  Manual,  Etc. 


LINICS  IN  OPTOMETRY"  is  a  unique 
work  in  the  field  of  practical  refraction  and 
fills  a  want  that  has  been  seriously  felt  both 
by  oculists  and  optometrists. 
The  book  is  a  compilation  of  optometric  clinics,  each 
clinic  being  complete  in  itself.  Together  they  cover 
all  manner  of  refractive  eye  defects,  from  the  simplest 
to  the  most  complicated,  giving  in  minutest  detail  the 
proper  procedure  to  follow  in  the  diagnosis,  treatment 
and  correction  of  all  such  defects. 

Practically  every  case  that  can  come  before  you 
is  thoroughly  explained  in  all  its  phases  in  this  useful 
volume,  making  mistakes  or  oversights  impossible  and 
assuring  correct  and  successful  treatment. 

The  author's  experience  in  teaching  the  science  of 
refraction  to  thousands  of  pupils  peculiarly  equipped 
him  for  compiling  these  clinics,  all  of  which  are  actual 
cases  of  refractive  error  that  came  before  him  in  his 
practice  as  an  oculist. 

A  copious  index  makes  reference  to  any  particular 
case,  test  or  method,  the  work  of  a  moment. 

BOUND   IN   SILK  CLOTH 
Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price 

$1.50  (6s.  3d.) 

Published   by 
THE  KEYSTONE   PUBLISHING   COMPANY 

809-811-813    NORTH   19th  STREET 
PHILADELPHIA,  U.  S.  A. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

Los  Angeles 

This  book  is  DUE  on  the  last  date  stamped  below. 


JUN  W^i1* 

JUN  14  REClO 


DEC  0  2 1988 
DEC  041988 


Form  L9-Series  4939 


3  1158  01043  2549 


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UC  SOUTHERN  REGIONAL  LIBRARY  FACILITY 


A  A      000190  951    4 


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